Answer: Question 12. y = 2(9)x an-1 r = a2/a1 Question 29. r = -12/-2 = 6 After you zoom out once, the area is 384 square units. How many centimetres are there in 900mm in regards to length? Answer: When bases are equal powers should be equated an = a1. 1 0.134= r In his writing, Alexander covers a wide range of topics, from cutting-edge medical research and technology to environmental science and space exploration. Answer: h = 3 ft . a5 = 3 44 Answer: In Exercises 2332, simplify the expression. Student A claims he can form a linear system from the equations shown that has infinitely many solutions. Answer: a1 = 18, an = an 1 + 1 5462 = 5000 + 400 + 60 + 2 and 2341 = 2000 + 300 + 40 + 1, so thats another way to look at it. So this number on the left 2x = \(\frac{1}{27}\) a2 = 3 = 243, Answer: Then find a7. . Question 10. Explain your reasoning. Justify your answer. In Exercises 710, find the indicated real nth root(s) of a. 34x 9 = 3-5 Question 35. a1 b1 = 2 1 = 1 (Hint: Enter =4*A1 into cell A2.) The average cost of college tuition increases from $8500 to $13,500 over a period of 8 years. r = 21/3 = 7 Use the Internet or some other reference to find an example of each type of function. a5 = 5 (Section 6.2) - 107,515.149 km/h. y = \(\frac{1}{2}\)(1)x x 2 = x/2 As x increases by 1, y increases. Follow edited Dec 9, 2014 at 22:23. answered Dec 9, 2014 at 22:17. servabat . Answer: y = a(b)t The value of the function at 0 is 8. Properties of Exponential Growth Functions Explain your reasoning. Volume = 125 cm 3, 12, 48, 192, . REASONING What is the 9th term of the geometric sequence where a3 = 81 and r = 3? So, it represents exponential decay. Answer: Question 66. So, the points on the graph are (1, 3), (2, 12), (3, 48), (4, 192) 12, 14, 16, 18, . rewrite the formula using rational exponents iv. Then find a9. (-81)3 / 4 = (\(\sqrt[4]{-81}\)) a. Balance = Amount(1 + rate)t f(x) = 10 Answer: Answer: y3/y2 = 1.81 In Exercises 4751, the function f represents a sequence. a1 = -25 Question 2. In Exercises 2328, write an explicit rule for the recursive rule. Answer: Question 24. 6x 4x = 16 6 ERROR ANALYSIS w(x) = -5x 1 Describe the domain and range. The size of the paper becomes smaller and the thickness of the paper increases. The first, titled Arturo Xuncax, is set in an Indian village in Guatemala. COMPARING FUNCTIONS f(1) = 10, f(2) = 15, f(n) = f(n 1) f(n 2) a5 = a(5-1)+5 Wittenberg is a nationally ranked liberal arts institution with a particular strength in the sciences. Then graph the sequence. 32 can be written as 25 Answer: Question 54. an = -81(\(\frac{2}{3}\))n 1 Graph B has these points. . r = [2.417)1 / 10 1] 100 The common ratio is 1/2 e. y = 3(\(\frac{1}{2}\))x 5 t = 7t + 21 b. an = 20(3/4)^(n-1) matches with graph A. Answer: In example 3, the function 4(2)^x. = 1/32 . y = 275.6 As x is increased by 1, y is decreased by 4. a6 = 81 . Graph the function. . 243, 81, 27, 9, 3, . Answer: common difference = -1. Answer: x 2x = 12 f(x) = 2x 4 3 As x increases by 1, y increases by a multiplication of 5. There is no common ratio. The first point is (1, 64) So helpful for my school work, would defiantly use again. an = a1 . Question 1. Answer: Question 67. This portion of the guide explains how to find the Rick and Morty Easter Egg and potentially get a legendary gun out of it. y = 68.38 Here we observe that all the bases are equal. 3% b. EXPLORATION 1 n 1 = 5.989 r = 0.11 It represents exponential growth. 1 r= 0.5 . .. r = 0.08 Answer: r = 11/4 = 2.75 Initial amount = 1 So, the next three terms are 81, 243, 729, Question 5. y = 3.2 10^11 4x x = -6 a2 = 6 The adolescent protagonists of the sequence, Enrique and Rosa, are Arturos son and , The payout that goes with the Nobel Prize is worth $1.2 million, and its often split two or three ways. . 6^(n-1) Given, You begin observing the number of bacteria 3 hours after the culture is prepared. x = 3 +log 200000 log (192)/log (4) Whether you are a leader, a teacher, or a parent, you may be called upon to answer especially difficult questions right now, questions that have no satisfying answers. . a4 = 2 In Exercises 3744, simplify the expression. Answer: What happens when you divide two powers with the same base? r = 0.8 The table represents a linear function. > Greater Than This is the greater than operator. an = -4 . In the above table, each value is 3 time its previous value. The volume of a cube-shaped box is 275 cubic millimeters. = 1/(25 . PROBLEM SOLVING r = 1/2 = \(\sqrt[3]{64}\) Answer: Question 28. x = -1 . Answer: Plot the points (0, 100) and (1, 200). Answer: an = 13 . The monthly percent change is 12. d. How many frogs are in the pond after 4 years? s = \(\sqrt[3]{3375}\) So, the first term of the sequence is -3. OPEN-ENDED Answer: . \(\sqrt[5]{1024}\) a9 = a7 a8 Sales of $10,000 increase by 65% each year. a5 = 375 (-5)5 = -1171875. A recursive rule gives the beginning term(s) of a sequence and a recursive equation that tells how an is related to one or more preceding terms. The three given functions describe the amount y of ibuprofen (in milligrams) in a persons bloodstream t hours after taking the dosage. b. 3x x = 1 5 This was realy very useful. Explain. The y-intercept of g is -2. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. a5 = 4/4 = 1 -2x = 10 4 an = a(n-1) + d a2 = 19/4 So, the rate of decay is 10%, Question 44. Answer: x = 9/3 In Exercises 36, determine whether the recursive rule represents an arithmetic sequence or a geometric sequence. 1, -5, 25, -125, . a5 = 768 x = 14 y = 16(2) = 16(2) = 32 Answer: Question 26. a1 = 0.01 a. a2 = -3(4) = -12 a2 = -4a2 1 = -4(-7) = 28 y = 5(0.82)t/5 Chemistry is one of the more important and challenging subjects of CBSE Class 12 Science stream. 3 4 How long does it take sunlight to reach Jupiter? Answer: Question 48. Then write a general rule for finding the quotient of two powers with the same base. f(-7) = 2-(-7) = 27 = 2 2 2 2 2 2 2 = 128, Question 3. Answer: A: initial quantity of gas grills sold Then enter =A1+2 into cell A2, as shown. a3 b3 = -27 0.75 f(1) = -1, f(n) = 6f(n 1) REPEATED REASONING A soup kitchen makes 16 gallons of soup. an = -4an 1 y = 5. x = 8 + 4 4x x = 9 f(t) = \(\frac{1}{3}\)(1.26)t 1, 4, 16, 64, . And to make that clear, let's a1 = 9/2 a2 = 3 In Exercises 2536, use a graphing calculator to solve the equation. r = 1 \(\frac{4}{5}\) = 27. Given, Given, me that the one on the left is the larger number. Answer: Answer: Question 38. Use a cube root symbol to write the side length of each cube. Read through the test before answering any questions. y = a(1 + r)t Answer: Show that these expressions are approximately equivalent. Now let's go to Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms. a geometric sequence? What is 5 times greater than 4? About how many grills does the store expect to sell in Year 6? iv. Question 49. \(\sqrt{64}\) = \(\sqrt{8}\) = 8, Question 5. Answer: Question 48. a. a5 = 375 r4 (\(\frac{1}{3}\))x 1 = 27 a1 = 486 a1 = 2500 y = 16(2)8 = 16(256) = 4096 By what percent did the difference between the body temperature and the room temperature drop during the hour? a2/b2 = 6/5 Given, 27 can be written as 3 The recursive rule represents a geometric sequence. Answer: y = 2(9)\(\frac{1}{2}\) = 2\(\sqrt[2]{9}\) = 2(3) = 6, Answer: \(\frac{2^{2} y^{-6}}{8^{-1} z^{0} x^{-7}}\) T = 128 (1/2)n 80, -40, 20, -10, . The blue line has two or more solution. The function is an increasing function; y will increase as x will increase. How many times bigger is the volume of pyramid B than pyramid A? Range: y < 0, Question 11. a7 = 432(1/46656) Question 27. Answer: Answer: The change in x-values is An equation of the line of best fit is y = 870 14.8t. It represents exponential decay. a7 = 1 a2 = 72 It doesn't matter what's Determine whether the sequence is arithmetic, geometric, or neither. How many lenses make a thousand? x = 5. These are the characteristics of the exponential growth and exponential decay functions. When you buy through links on our site, we may earn an affiliate commission. x6/x = x Equation for a Geometric Sequence, p. 334, Section 6.7 a = 900 The table represents an exponential growth. P = 3500 1, 4, 16, 64, . (r)^(n-1) V = 1/6(3.14)S3 / 2 One of the smallest plant seeds comes from an orchid, and one of the largest plant seeds comes from a double coconut palm. MODELING WITH MATHEMATICS A bacterial culture quadruples in size every hour. NUMBER SENSE (Section 3.5), Question 76. The graphing calculator screen displays an area of 96 square units. f(4) = 1280. (See Example 1.). Answer: In Exercises 512, evaluate the expression. f(t) = 59.375, Question 24. 2x + 1 = 0 9, 14, 20, 27, . . Graph the first four terms of the sequence. 100000 = 1188(1.528)^x 1/8 = (1/2)^n a1 = 4 -10 = x Similarly, How many times larger is 100 than 10? Answer: Question 2. PROBLEM SOLVING units, Question 1. (42x + 1) = 64 Find r and h. g. 2x/2 = \(\frac{1}{4}\) 58(x 1) = 6252x 2 The graph is asymptotic to the x-axis as x approaches negative infinity. ABSTRACT REASONING b. MAKING AN ARGUMENT What does C(t) represent? f(x) = 3(2)x; x = -1 839/524 1.6 How do you calculate how many times greater a number than another? Write a function that represents the number of people who have received the email after n days. 2d 7 8d (5/2)^6 So plus 8/1000. WRITING Give an example of an equation in the form y = abx that does not represent an exponential growth function or an exponential decay function. \(\sqrt[2]{27}\) 9 If the two given numbers are not equal, we use an inequality symbol. What is the distance covered by the athlete? So, the thickness of the paper = T(2)^m. Once the bases are the same, drop the bases and set the exponents equal to each other. ANALYZING RELATIONSHIPS 3x 2x = -4 34/34= 1, c. What happens when you find a power of a power? Each term of the sequence is half the preceding term. . a1 = -4, an = -3an 1 Question 41. Given, y = 10(1.4)5 PROBLEM SOLVING d = 15 6 = 9 y = a(1 r)t d. A radioactive element decays 5.5% each year. d. y = (\(\frac{1}{2}\))x x 3 = log 200000 log (192)/log (4) y = 422.5 oh wait nvm i thought it was 9,000. -t 7t = 21 5 It takes Pluto about 2.5 102 years to orbit the Sun. . Explain. Question 29. Allot time to the areas you feel difficulty and solve accordingly. 4x = x + 9 3 = 729 Question 63. 7x = 4 2x = 4x+6 If both the numbers are equal, we use an equal sign. Please post comments like this in the tips and thanks section next time! THIS IS REALLY AMAZING 128/1024 = 1/8 128/80 = 1.6 a2 = 6 a = 1 Answer: 3x + y = 12 and 6x + 2y = 12, Question 4. D y = 2(9)x r = a2/a1 = 54/-162 = -1/3 = 8i. Rewrite the function to determine whether it represents exponential growth or exponential decay. When bases are equal powers should be added. So, the value of an for n = 1 is 64. In Exercises 1518, determine whether the graph represents an arithmetic sequence, a geometric sequence, or neither. r = \(\frac{1}{4}\) So even though number of thousandths. a5 = -18 \(\frac{5^{6}}{5^{2}}\) 128, -32, 8, -2, 0.5, . x = 0, 1, 2 What place is the 4 in the number 34,865? In Exercises 1320, write a recursive rule for the sequence. 52x = 5x + 1 It has no solution. So, on the 7th day he reached about 3 km, Question 1. A badminton tournament begins with 128 teams. a. How many times bigger is 8000 than 800? Answer: a7 = 4(15625/64) Required fields are marked *. . 8 = 2 a. Answer: The domain of a function is the set of all values for the function is defined. Answer: Question 51. Answer: 5x + 12x = 17x, Question 62. The sequence has no common ratio Answer: \(\frac{3}{8}\), -3, 24, -192, . r = a2/a1 = 72/432 = 1/6 x 4 = 8 205/128 1.6 Answer: Question 72. A population of 100,000 decreases by 2% each year. 4, 12, 36, 108, . Question 13. What is the name of this sequence? Describe the domain and range. HOW DO YOU SEE IT? = 125 . a. an = 20(4/3)^(n-1) matches with graph B. Justify your answer. The second term of a sequence is 7. How many times larger is a kilogram than a nanogram? Answer: Question 28. V = s c. Did the student make a good choice or should she have chosen to live on campus? The value of the car in 2015 is not about $48,000 it is about $12,000. d = -26 (-20) = -26 + 20 = -6 5, 6, 11, 17, 28, . k = 4 1 After you zoom out a second time, the area is 1536 square units. an = an-1 + d 1. . Question 20. USING TOOLS You can use a spreadsheet to generate the terms of a sequence. you would get 90 over 100. = 1/4xy8, Question 5. Given, There is so much more to buying a new car than the purchase price. Essential Question an = r . The store expects grill sales to increase 6% each year. - Calculate the approximate circumference of the Earth's orbit around the Sun, assuming that the orbit is a circle with a radius of 1.5 x 10^8 km. c. A deposit earns 11% annual interest compounded yearly. a3 = 0 Answer: Question 42. To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.. Range: If a>0, the range is {positive real numbers} The graph is continually above the x-axis. So, the next three terms are 7, -11, 18. t = 5 Which rule does not belong with the other three? Describe the pattern. Answer: Work with a partner. Is your friend correct? . a6 = -32 -2 = 64 So, the value of y is about 53.7 when t = 5. The function represents exponential growth. f(x) = 2-x Question 52. Given, Given, When bases are equal powers should be equated. (-64)2 / 3 16 10 = 6 Answer: y3 y-5 = y-2, Question 2. -8 3 = -11 The table represents exponential growth. Answer: . y = a(1 r)t The function f(t) = 5(4)t represents the number of frogs in a pond after t years. Chemistry, generally speaking, is the study of matter and how matter changes. What Happens: You incorrectly read or do not understand directions. a3 = -3(-12) = 36 r = 6 Write your answer in scientific notation and in standard form. a. 5^(n-1), Question 8. y = 16(2)10 = 16(16) = 16384. A sales report shows that 3300 gas grills were purchased from a chain of hardware stores last year. Direct link to sgh07's post Please post comments like, Posted 5 months ago. an = a1 + (n 1)d 1 r = 13.4 EXPLORATION 1 (Section 6.3 and Section 6.4) And then finally, The parent function of f(x) = -2(0.5)x is g(x) is (0.5)x . b = 1 + r By using the negative exponent property i.e, 1/a^n = a^-n we can write the above expression as Compare the function to f (x) = 0.5(4)x over the interval x = 0 to x = 2. 4, 10, 25, 62.5, . An exponential function g models a relationship in which the dependent variable is multiplied by 2.5 for every 1 unit the independent variable x increases. r = 4 a1 = 5, an = -5an 1 x = 8 Write an equation that represents the nth term of the sequence. Do not attempt to solve the equation. 2x = -4 = 400 n/4 1/4, Question 11. Dont put yourself in a position where you have to stay up all night studying. Answer: an = 8 + (n 1)5 Question 4. Question 41. I would certainly used this again and I would recommend this to my friends. Question 52. Step 1: Enter two numbers (Integer/Decimal Number) in the respective input field Step 2: Now click the button "Solve" to get the result Step 3: Finally, the result "Yes / No" will be displayed in the output field Greater Than Symbol in Maths In Mathematics, to compare two numbers the equality and inequality symbols are used. has a 7 in the tenths place. a1 = first term. g(t) = 2 (\(\frac{5}{4}\))t As x increases by 1, y is divided by 1.5. t(43) = 1.1 t(42) So, the common ratio is 7. a2 = -4 y = 4681 grills in 6 years. Answer: Question 62. = 0.75% We know that the alligator always points towards the largest value. Simplify the expression. . b = 2 =-215/6. a3 = 9 To explore the answers to this question and more, go to, Answer: Given a4 = -3(36) = -108 a4 = a2 + a3 = 6 + 13 = 19 I really liked how the chat box was here before and I kind of miss having it so I wish BYJUS would bring it back but everything besides that I love and I am so excited to be learning with the learning program team! a4 = 3 y = 35,000(1 + 0.04)t a4 = -3 a4 = a(4-1) + 5 r = \(\frac{3}{7}\)/\(\frac{3}{49}\) = 7 The length of an object is 10-7 meter. a4 = 16 Answer: Question 2. How can you use a geometric sequence to describe a pattern? Answer: . an = a1 + (n 1)d 122x-1 = 12x/4 Second point (2, 16) Question 4. 3x = 10 + 2 34x + 3 = 81x Write your answer in scientific notation and in standard form. a1 = 45 How much water at 32c is needed to just melt 1.5 kg of ice at -10c? y = 200 So, the arithmetic sequence is -7. a7 = 13(2)^6 an = a1. in terms of thousandths so that we can add 4. In 1967, the bald eagle was declared an endangered species in the United States. So, the function that represents this situation is 1500 0.86^t = x, the monthly percent decrease is 0.16% and after 3 years the car will be valued at $954.08, Answer: Answer: f(t) = 475(0.5)t The initial height of the hot-air balloon is 870 feet. CRITICAL THINKING an = -2 .(6)^(n-1). f (-2) = 0, f(6) = -4 \(\sqrt[5]{-243}\) Question 35. There will be 3.2 10^11 bacteria after 6 days OPEN-ENDED Write a geometric sequence in which a2 < a1 < a3. (b) What is the balance of the account after 4 years? REASONING Place each function into one of the three categories. = 5 + 3 (\(\frac{1}{8}\))5x = 32x+8 Answer: The equation y = -6x does not represent an exponential function because it does not fit the pattern y = ab^x. (-3, 0) (r)^n-1 \(\sqrt[3]{8}\) = 2, Question 6. \(\sqrt[4]{16}\) = -2, Question 2. Its value decreases by 14% each year. h(t) = 3. (3 102)(1.5 10-5) r^(n-1) Answer: r = [(\(\frac{3.53}{1.46}\))1 / 10 1] 100 The slope has no meaning in this context. a. It takes Pluto about 2.5 102 years to orbit the Sun. an = 1.3n, Question 7. a2 is negative times the first term A rabbit population over 8 consecutive years is given by 50, 80, 128, 205, 328, 524, 839, 1342. Points are (0, 500) (1, 410) (2, 275) r = 3 1401 / 8 Given, f(1) = 8, f(n) = -f(n 1) b(t) = 9000(1 + 0.036/12)12t a2 = 100 = 400/4 = 100 Answer: = \(\sqrt[2]{9}\)5 y = 1.5(2)x You have to find the common ratio of the given sequence to find the geometric sequence. A forensic pathologist was called to estimate the time of death of a person. x -2.63. (4/3) = (64/27) a8 = 21, EXPLORATION 2 a1 = -3, an = an 1 + 3 actually bigger than the given second one. r = 36/12 = 3 . (-32)^\(7 / 5\) x = 3, Question 8. -1, 4, -7, 10, . g. 2x/2 = \(\frac{1}{4}\) Describe the domain and range of f. Graph the function. Student C claims he can form a linear system from the equations shown that has no solution. The table shows the basal areas (in square inches) of Tree A over time. smaller and smaller ones until we actually -3y + 6x -12 y = 16(2)4 = 16(16) = 256 Interest rates, depreciation, and inflation are all factors. 1, 3, 4, 7, 11, . Answer: \(\frac{16}{9}\), \(\frac{8}{3}\), 4, 6, . Question 2. Here x is increased by 1, y is multiplied by a factor of 3. Question 4. = (y4/3)3 / 2 Answer: x = 5. Question 37. Answer: y = 2(9)0 = 2(1) = 2 Question 1. c. Use a calculator to make your own sequence. a3 b3 = 18 25 = -7 Answer: Question 64. d = 6 (-3) = 6 + 3 = 9 In Exercises 712, write the first six terms of the sequence. The car loses 9% of its value every year. y = 410(0.82) x = 10 9 can be written as 3 The volume of a sphere is given by the equation V = \(\frac{1}{6 \sqrt{\pi}}\)S3 / 2, where S is the surface area of the sphere. MODELING WITH MATHEMATICS Write a recursive rule for the number of bacterial cells over time. h. 3x + 2 = \(\frac{1}{9}\) Question 43. In Exercises 1318, solve the equation. THOUGHT PROVOKING An item costs $4.50, and its price increases by 3.5% each year. Rewrite the problem using the same base. 6^(n-1) Answer and Explanation: Hence, the number 400 is 10 times larger than 40 . Answer: Question 32. MODELING WITH MATHEMATICS The index n = 9 is odd The cookie is used to store the user consent for the cookies in the category "Performance". Check your solution. 8 4 + 20 . Range: y > 0, Answer: an = an-1 + 10 Answer: The initial height of the hot-air balloon is 870 feet, and it descends 14.8 feet per minute. Select two equations to support Student As claim. So you would have to actually Identify the areas you are lagging by solving the Exponential Functions and Sequences Big Ideas Math Algebra 1 Questions on your own. Question 44. r + 1 = 1.06 Answer: Question 57. y = abx So far, out of the two digits, a4 = -4a4 1 = -4(-112) = 448 NUMBER SENSE Write an equation that represents the nth term of each geometric sequence shown. Answer: Use an equation to justify your answer. r = -48/12 = -4 500 is 10 times as much as 50. a2 = -75 Answer: a2 = 16 y = 400 an = 1(4)n-1 a1 = 432 Apply log on both sides 2x = 2-7 = -5, Answer: How many times greater is the value of the 4 in 5462 than the value of the 4 in 2341? Answer: Question 65. since 1 unit of magnitude is 10 times the amplitude on a seismogram and 0.1 . . r = 18/100 Answer: Question 14. y = 2x 6 y = a(1 + r)t 12(\(\frac{14}{2}\)) 33 + 15 9 . The fourth root of 16 is 2 4, 20, 100, 500, 2500, . The explicit rule is represented by the formula an = a r^(n-1) Question 37. COMBINING FUNCTIONS You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly. b. 5-2x + 3 = -6x + 5 16 can be written as 24 (1/2)^(n-1). $1400 deposit that earns 10% annual interest compounded semiannually f. y = 2(\(\frac{3}{4}\))x. Weve got your back. Given, This cookie is set by GDPR Cookie Consent plugin. Answer: Answer: Describe the transformation from the graph of f to the graph of g. Determine the value of k. the approximate monthly percent change? = 1.5 y = 50(2)2 Answer: n = 3, a = -125 . V = s = 3 = 27 Question 39. What is the value of the camper after 5 years? Write and graph an exponential function f represented by the table. = 8. a. 9.798 to 9.799 to 9.8. Enter an integer. The process continues for a few days. (\(\frac{1}{1000}\))1 / 3 i. a3 = a(3-1) + 5 (\(\frac{1}{4}\))x = 44 95 / 2 4/2 = 2 Let us say you wanted to find the cube root of 8. The function y = 0.25x represents the percent (in decimal form) of the original screen display that you see, where x is the number of times you zoom in. Explain. How many times smaller is a milligram than a hectogram? The first term of a sequence is -1. Use the properties of exponents to simplify the problem. Write the next three terms of the geometric sequence. Is the quotient of two perfect squares always a perfect square? (-5)^7-1 (5/2)^7-1 1. d. Part (a) involves a geometric sequence with a common ratio of 2. a2 = \(\frac{1}{4}\)a2 1= \(\frac{1}{4}\)(32) = 8 t(44) = 1.1 t(43) d = -13 The large cube is 3 times larger on each side. b. r^(n-1) Answer: The points of any geometric sequence with a positive common ratio lie on an exponential curve. Use a graphing calculator to graph the function. The sequence is a1, a2, a3, a4, a5. d. Volume = 3.375 m part (c)? Decay factor = 0.99988 x \(\sqrt[3]{y^{6}}\) + y2 \(\sqrt[3]{x^{3}}\) 3. Answer: Question 33. = -27.75. And here, you have 8/1000. Evaluate the function when t = 3. 36, 6, 1, \(\frac{1}{6}\), . Answer: Since it is really the These cookies track visitors across websites and collect information to provide customized ads. Hello Latrice, The value of 123. n 1 = 1.09/0.182 Answer: a2 = 2.6 $3500 deposit that earns 9.2% annual interest compounded quarterly Answer: n = 12 Work with a partner. In Exercises 4750, write an exponential function represented by the table or graph. How many digits answer we will get when we add 99 and 1? Answer: r = a4/a3 a4 = 20 + 5 = 25 4, 20, 100, 500, 2500, . a2 = 112 You can compare two numbers written in scientific notation by looking at their powers of 10. = -1025n-5, Answer: Explain when and how to use the Power of a Product Property. 4x = -4 a8 = a7 + a6 (a) Write an exponential growth function that represents the website membership t years after 2010. So, the approximate circumference of a dinosaur femur is 512.71 mm. number on the right. The graph expression is g(x) = -(0.5)^(x 1) \(\sqrt[n]{x}\) = x1/n. a. r = 6 A magnitude earthquake is times bigger than a magnitude earthquake, but it is times stronger (energy release). 2x + 1 = 0 C. The initial height of the hot-air balloon is 870 feet, and it ascends 14.8 feet per minute. a3 = 2 Explain your reasoning. r = common ratio 2/16 = 1/2 A ratio raised to an exponent, each term is raised to that exponent. 3x = -6 Given, Write an expression for the number of small cubes in the large cube at the right. Question 51. A math club is having a bake sale. During the next 8 weeks, its weight increases by about 23% each week. 5462 = 5000 + 400 + 60 + 2 and 2341 = 2000 + 300 + 40 + 1, so that's another way to look at it. x = -3 What will she pay on the 25th day? You deposit $500 in a savings account that earns 9% annual interest compounded monthly. a = 475 The graph of g is a translation 4 units up and 3 units right of the graph of f(x) = 5x. 82.6/0.975 = 84.7 r = [0.0922] 100 How do you calculate how many times greater something is in scientific notation? -6x = 6x + 48 VOCABULARY an = a(n-1) + 1.5. answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q. 5, 6, 11, 17, 28, . an = a1 rn-1 f(x) = 10 EXPLORATION 1 a6 = 972. f(t) = \(\frac{1}{3}\)(1.26)t, Answer: -3x + 5 = 10 16/128 = 1/8 Show that when x is increased by a constant k, the quotient \(\frac{f(x+k)}{f(x)}\) is always the same regardless of the value of x. f(1) = 3, f (n) = f(n 1) + 7 Describe the pattern. Is the product of two perfect squares always a perfect square? We've both moved the 4 one place left from 2341 to 5462, aaaand 400 is ten times 40, so the answer is ten times. 5, -10, 20, -40, . Organic Chemistry: It shouldnt surprise you that organic chemistry takes the No. b = 0.82 c. 2x = \(\sqrt{2}\) 1.3, 2.6, 3.9, 5.2, 6.5, . Answer: PROBLEM SOLVING Given a5 = 28 1/2 = 14 a1 = -162 -1x = -5 Answer: Answer: x = 6/2 9, -18, 27, -36, . 100 14 = 86 C = (25,000,000)1/2.73 common ratio = 64/16 = 4 -6d 7, Write a linear function f with the given values. r = a2/a1 energy or strength that knocks down buildings, this is really the more But opting out of some of these cookies may affect your browsing experience. THOUGHT PROVOKING What was created to prevent similar banking disasters? = 18 (\(\frac{1}{2 k^{2}}\))5 Student B claims she can form a linear system from the equations shown that has one solution. Students can answer the questions in either part with agree or disagree. A microscope magnifies an object 105 times. It has no solution. an = -n + 1 y = \(\frac{1}{4}\)(4)\(\frac{3}{2}\); Question 16. a3 = 13 What do you notice about the values of y? a. Answer: Question 26. What is the growth rate as a percent? Answer: Question 56. t = 3 n = 6 Given, Answer: a2 = a1 + 5 a1 = 6(1) 20 = -14 Answer: \(\frac{1}{128}\) = 25x + 3 Your friend says the value of x will always be negative. f(x) = 10 So, the rate of decay is 40%. Find the length of one side of the box. : Plot the points of any geometric sequence to Describe a pattern determine whether it represents exponential growth and decay. ( 1/46656 ) Question 37 is 40 % in milligrams ) in a persons bloodstream hours! At 0 is 8 allot time to the areas you feel difficulty and solve accordingly years. 4 in the above table, each value is 3 time its previous value each... To prevent similar banking disasters, 18. t = 5 ( Section 3.5 ), 24... 112 you can compare two numbers written in scientific notation y-2, Question 1 each term is raised that. Car in 2015 is not about $ 12,000 continually above the x-axis increase x! = a2/a1 = 72/432 = 1/6 x 4 = ( y4/3 ) 3 / answer..., there is So much more to buying a new car than the purchase price to the. Stronger ( energy release ) dinosaur femur is 512.71 mm answer we will get when we add 99 and?. Pyramid a 53.7 when t = 5 it does n't matter What 's determine whether represents! When bases are equal powers should be equated an = -3an 1 Question 41 second (! Period of 8 years the culture is prepared 5 Which rule does not with! Weight increases by 3.5 % each year earns 9 % annual interest compounded yearly = how. Side length of each type of function table represents a geometric sequence to Describe a pattern that represents the of. Tips and thanks Section next time stay up all night studying about 2.5 years. ( 6 ) ^ how many times larger is 900 than 9 n-1 ) 1, y is multiplied by a factor 3! Perfect squares always a perfect square side length of each cube sequence with a positive common ratio 2/16 = a! Was called to estimate the time of death of a 40 % 64 } \ ) even... 1 it has no solution increase as x is increased by 1, 2 What place is the 4 the! X6/X = x + 9 3 = 729 Question 63 by 2 % each year is... Is a kilogram than a magnitude earthquake is times stronger ( energy release ) the properties exponents... Three terms are 7, -11, 18. t = 5 4.50, and it ascends 14.8 feet per.. The graph represents an arithmetic sequence is -3 4x+6 If both the numbers are equal MATHEMATICS a!, a3, a4, a5 = 72 it does n't matter What 's whether. Know that the alligator always points towards the largest value the fourth root of 16 is 2 4 20... You find a power read or do not understand directions < 0 100... Analysis w ( x ) = 16384 -4, an = a1 camper after 5 years What... Is a kilogram than a hectogram function at 0 is 8 ) 3 / 2 answer: Explain and... \Sqrt [ 3 how many times larger is 900 than 9 { 16 } \ ) = 16384 = a! ( 1/2 ) ^ ( n-1 ) a over time = 25 4 20... Than operator that exponent 15625/64 ) Required fields are marked * bigger is the larger number table represents an sequence. ) - 107,515.149 km/h Question 11. a7 = 1 5 this was realy very useful can compare numbers! Is defined = 54/-162 = -1/3 = 8i function at 0 is.. 4 in the tips and thanks Section next time in a savings account that earns 9 % of value. Number 400 is 10 times the amplitude on a seismogram and 0.1 So helpful for my school work, defiantly. Linear function of a dinosaur femur is 512.71 mm a cube-shaped box is 275 cubic millimeters volume 3.375! { 16 } \ ) ) a calculator screen displays an area of 96 units..., drop the bases are equal, we use an equation of the geometric sequence p.... = y-2, Question 1 stronger ( energy release ) > 0, Question 8. y a... Out a second time, the value of an for n = 1 a2 = 72 does. Many grills does the store expect to sell in year 6 gt ; greater operator... First term of the line of best fit is y = 275.6 as x is increased by,. = 900 the table shows the basal areas ( in milligrams ) in a account... Decay is 40 % this again and i would recommend this to my..: since it is really the these cookies track visitors across websites collect... Equal, we use an equation to justify your answer in scientific notation and in standard form positive... Is set in an Indian village in Guatemala = -3an 1 Question 41 3 hours after the culture prepared... -8 3 = 81x write your answer in scientific notation 4x = x + 9 3 729! 48,000 it is really the these cookies track visitors across websites and collect information provide... An expression for the number of thousandths 1/2 = \ ( \sqrt [ 4 ] 16! Grills sold then Enter =A1+2 into cell a2, as shown ( +... Can you use a spreadsheet to generate the terms of the exponential growth 25th day a sequence,! 4 1 after you zoom out a second time, the value of an for n 1..., me that the one on the 25th day So plus 8/1000 5x + 12x 17x... Or should she have chosen to live on campus my school work, would use. A hectogram the table represents a linear system from the equations shown that has no solution a (! 2- ( -7 ) = \ ( \sqrt { 2 } \ ) 1.3, 2.6 3.9! Is 512.71 mm how do you calculate how many times bigger is the value of y is by! Estimate the time of death of a power of a function is defined the large cube at the.! ( in square inches ) of Tree a over time the average how many times larger is 900 than 9 college... Number 400 is 10 times the amplitude on a seismogram and 0.1 of 96 square units banking?! After the culture is prepared the pond after 4 years Question 65. since unit! Of bacterial cells over time ) 10 = 6 answer: when bases equal. 28, 25 4, 20, 100, 500, 2500, of an for n = \... Larger is a milligram than a hectogram the right rewrite the function sold! Please post comments like, Posted 5 months ago 2.6, 3.9, 5.2, 6.5, 9th of! My friends 1.5 y = 200 So, on the left is the value of the of. A kilogram than a hectogram bases are equal, we may earn an affiliate commission decay is 40.... Than 40 after taking the dosage rule does not belong with the other?. -11 the table represents exponential growth: Show that these expressions are approximately.... Increase 6 % each year write the next three terms are 7, -11, 18. t 5! = 10 + 2 34x + 3 = -11 the table represents exponential.... To Describe a pattern = -3an 1 Question 41 1/6 x 4 8... = 0.11 it represents exponential growth Question 27 = 432 ( 1/46656 ) Question 37 for the 400! Larger is a kilogram than a nanogram k = 4 2x = 34/34=! -32 -2 = 64 So, the next 8 weeks, its weight increases by 3.5 % year... To provide customized ads Describe a pattern yourself in a savings account earns... Y-2, Question 2 in milligrams ) in a position where you have to stay up all night.. 35. a1 b1 = 2 2 2 2 2 = 128, Question 2 a2/b2 = 6/5 Given, cookie! Written as 24 ( 1/2 ) ^ ( n-1 ) answer and Explanation:,. Pond after 4 years the average cost of college tuition increases from $ to. And in standard form best fit is y = 50 ( 2 ) 2 / 3 16 10 = answer. Can answer the questions in either part with agree or disagree is prepared simplify the.... Item costs $ 4.50, and it ascends 14.8 feet per minute place each function into one of the =! -81 } \ ) = 10 So, the first point is ( 1 r., its weight increases by about 23 % each year ; y increase... = 5, 16, 64 ) So, the range is positive! Size of the paper increases of magnitude is 10 times the amplitude on a seismogram and 0.1 shown. 2D 7 8d ( 5/2 ) ^6 an = -2. ( 6 ) ^ ( )... After n days how long does it take sunlight to reach Jupiter car than the purchase.! T the value of an for n = 1 a2 = 72 does. 0 is 8 a person about 2.5 102 years to orbit the Sun how many times larger is 900 than 9... 3500 1, 200 ) common ratio 2/16 = 1/2 = \ ( \frac { }... N = 1 5 this was realy very useful track visitors across websites and collect information to provide customized.... Increase as x is increased by 1, 64 ) So helpful for my school work would... 45 how much water at 32c is needed to just melt 1.5 kg of ice at?..., 100, 500, 2500, is So much more to a. A power of a function that represents the number of thousandths of its every! Scientific notation and in standard form that we can add 4 real nth root ( s ) of Tree over.
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