Math 3201 Chapter 6 Review

Transcription

1 Math 0 Chapter 6 Review Multiple Choice Identif the choice that best completes the statement or answers the question.. Which of the following is an exponential function? A. f(x) = x B. g(x) = ( ) x C. h(x) = 7 x D. j(x) = x. Match the following graph with its function. x A. = (0.) x B. = (.) x C. = 0.() x D. = (0.7) x. Match the following graph with its function. x A. = (0.) x B. = (.) x C. = 0.() x D. = (0.7) x. Identif the range of the exponential function = 0 x. A. { < 0, R} B. { > 0, R} C. { 0, R} D. { R}

2 . Determine the -intercept of the exponential function f(x) =. A. 0 B. C. D. 6. Which option best describes the behaviour of the exponential function f(x) =? A. increasing because a > B. decreasing because 0 < a < C. increasing because b > D. decreasing because 0 < b < 7. Express as a power with a base of. A. B. C. D. 8. Express as a power with a base of. A. B. C. D. 9. Solve the following exponential equation b writing both sides with the same base. A. x = B. x = C. x = D. x = 0. Solve the following exponential equation b writing both sides with the same base. A. z = 7 B. z = 8 C. z = 9 D. z = 0. The population of a specific bacteria growing in a Petri dish is modelled b the function where P(t) represents the number of bacteria and t represents the time, in das, after the initial time. How long does it take for the population to double? A. da B. das C. das D. 9 das

3 . The following data set involves exponential growth. Determine the missing value from the table. x A. 6. B..00 C. 7.0 D Determine the equation of the exponential regression function for the data. x A. = 7(0.8) x B. = 7(.6) x C. = 60(0.8) x D. = 60(.6) x. A scatter plot is drawn using a data set x Identif the equation of the curve of best fit. A. = (.) x B. = (0.) x C. = (.) x D. = (0.) x. The equation of the exponential function that models a data set is = 6.8(.0) x Determine the range of this function. A. { > 0, R} B. { R} C. { > 6.8, R} D. { >.0, R} 6. An investment can be modelled b the following growth function, where x represents the time in ears: = 00(.08) x What was the principal invested? A. $0 B. $00 C. $8 D. $08

4 7. An investment can be modelled b the following growth function, where x represents the time in ears: = 00(.08) x What was the annual interest rate for the investment? A. % B..08% C. 8% D..8% 8. Eli invested $000 at %/a compounded quarterl. Define an exponential growth function for this investment in the form A(n) = P( + i) n where n represents the number of compounding periods. A. A(n) = 000(.00) n B. A(n) = 000(.007) n C. A(n) = 000(.0) n D. A(n) = 000(.0) n 9. Denis recentl spent $80 on a new laptop for his home business. He read that the depreciation rate for this model laptop is %. How much mone should Denis expect to sell his laptop for in three ears? Short Answer A. $0 B. $960 C. $0 D. $70. Sketch the exponential function f(x) =.. Solve the following exponential equation b writing both sides with the same base. =. Solve the following exponential equation b writing both sides with the same base. e =.. A research lab has a mg sample of a radioactive substance. The amount of the substance, A(t), left in the sample can be modelled b the half-life function x where t represents the time, in das, after the initial time. How long does it take for the sample to reduce to one quarter its initial amount? t = 70. Determine whether the following data set involves exponential growth, exponential deca, or neither. Explain how ou know. x The fish population in Loon Lake is modelled b the equation P(t) = 00(0.9) t where P(t) represents the number of fish and t represents the time, in ears, since 00. Estimate the fish population in 00. Population = 7 7. Complete the table of values for a $0 investment earning.%/a compounded monthl. Time (months) 0 Value ($)

5 mlkk 8. An investment can be modelled b the following growth function, where x represents the time in ears: = 77(.0) x What was the annual interest rate for the investment?.% 9. Nevia invested $000 at.%/a compounded weekl. Define an exponential growth function for this investment in the form A = 000( ) n A(n) = P( + i) n where n represents the number of compounding periods. 0. Pavendeep recentl spent $6 00 on a new car. He read that the depreciation rate for this model of car is %. How much mone is Pavendeep s car worth in 6 ears? $667.6 Problem. Which exponential function matches each graph below? Provide our reasoning. i) iii) B ii) A iv) a) b) x x. A vehicle was purchased for $ 000 in 00. The book value of the vehicle can be modelled b the exponential function where represents the value in dollars and x represents the time, in ears, after 00. a) How does the value of the vehicle change over time? Explain how ou know. Depreciates b 8%/a b) Estimate the value of the vehicle in 0. Show our work. $06.7. Solve the equation and verif our answer b substitution. Show our work. x=. Solve the equation and verif our answer b substitution. Show our work. x =. Thorium-7 has a half-life of 8. das. The remaining amount of a 0-mg sample of thorium- 7 can be modelled b the equation where A(t) is the amount of thorium-7 remaining, in milligrams, and t is the time in das. a) Determine the amount of thorium-7 remaining after 0 das, to the nearest milligram. Show our work. mg

6 b) Determine the amount of thorium-7 remaining after 00 das, to the nearest tenth of a milligram. Show our work. x =.6 mg

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