1. How many x-intercepts does the exponential function f(x) = 2(10) x have? B. 1 C. 2 D. 3

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1 Multiple Choice 1. How many x-intercepts does the exponential function f(x) = 2(10) x have? A. 0 B. 1 C. 2 D How many y-intercepts does the exponential function f(x) = (5) x have? A. 0 B. 1 C. 2 D Which of the following is an exponential function? A. f(x) = x 2 B. g(x) = ( 1) x C. h(x) = 17 x D. j(x) = 2 3 x 4. Match the following graph with its function. A. y = 3(0.5) x B. y = 2(1.25) x C. y = 0.5(3) x D. y = 2(0.75) x 5. Match the following graph with its function. A. y = 3(0.5) x B. y = 2(1.25) x C. y = 0.5(3) x D. y = 2(0.75) x June

2 6. Identify the range of the exponential function y = 10 x. A. {y y < 0, y R} B. {y y > 0, y R} C. {y y 0, y R} D. {y y R} 7. Determine the y-intercept of the exponential function f(x) =. A. 0 B. 1 C. 2 D Determine the y-intercept of the exponential function h(x) = e x. A. 0 B. 1 C. 2 D Which option best describes the behaviour of the exponential function f(x) =? A. increasing because a > 1 B. decreasing because 0 < a < 1 C. increasing because b > 1 D. decreasing because 0 < b < Which option best describes the behaviour of the exponential function g(x) =? A. increasing because a > 1 B. decreasing because 0 < a < 1 C. increasing because b > 1 D. decreasing because 0 < b < Express as a power with a base of 10. A. B. C. D. 12. Express as a power with a base of 2. A. B. C. D. 13. Express as a power with a base of 3. A. B. C. D. June

3 14. Solve the following exponential equation by writing both sides with the same base. A. x = 2 B. x = 3 C. x = 4 D. x = Solve the following exponential equation by writing both sides with the same base. A. n = 0 B. n = 1 C. n = 2 D. n = Solve the following exponential equation by writing both sides with the same base. A. x = 1 B. x = 2 C. x = D. x = 17. Solve the following exponential equation by writing both sides with the same base. A. z = 7 B. z = 8 C. z = 9 D. z = Solve the following exponential equation by writing both sides with the same base. A. x = 2 B. x = 2 C. x = 4 D. x = Solve the following exponential equation by writing both sides with the same base. A. z = 0 B. z = 1 C. z = 2 D. z = The population of a specific bacteria growing in a Petri dish is modelled by the function where P(t) represents the number of bacteria and t represents the time, in days, after the initial time. How long does it take for the population to double? A. 1 day B. 2 days C. 3 days D. 9 days June

4 21. The population of a specific bacteria growing in a Petri dish is modelled by the function where P(t) represents the number of bacteria and t represents the time, in days, after the initial time. Determine the time when the population is A. 3 days B. 6 days C. 9 days D. 24 days 22. The following data set involves exponential growth. Determine the missing value from the table. x y A. 72 B. 96 C. 104 D A scatter plot is drawn using a data set. Identify the equation of the curve of best fit. A. y = 12(1.3) x B. y = 12(0.3) x C. y = 4(1.5) x D. y = 4(0.5) x 24. A scatter plot is drawn using a data set. Identify the equation of the curve of best fit. A. y = 4.8(1.08) x B. y = 4.8(0.81) x C. y = 8.4(0.81) x D. y = 8.4(1.08) x June

5 25. The equation of the exponential function that models a data set is y = 78.20(0.87) x Interpolate the value of y when x = 5.5. A B C D The equation of the exponential function that models a data set is y = 78.20(0.87) x Determine the domain of this function. A. {x x > 0, x R} B. {x x R} C. {x x > 78.20, x R} D. {x x > 0.87, x R} 27. The equation of the exponential function that models a data set is y = 6.8(1.03) x Extrapolate the value of y when x = 22. A B C D The equation of the exponential function that models a data set is y = 6.8(1.03) x Determine the range of this function. A. {y y > 0, y R} B. {y y R} C. {y y > 6.8, y R} D. {y y > 1.03, y R} 29. An investment can be modelled by the following growth function, where x represents the time in years: y = 2500(1.018) x What was the principal invested? A. $1250 B. $2500 C. $18 D. $ An investment can be modelled by the following growth function, where x represents the time in years: y = 2500(1.018) x What was the annual interest rate for the investment? A. 25% B % C. 18% D. 1.8% 31. An investment can be modelled by the following growth function, where x represents the time in years: y = 2500(1.018) x How long, in months, did it take for the account to reach $3000? A. 10 B. 123 C. 28 D. 94 June

6 32. An investment can be modelled by the following growth function, where x represents the time in years: y = 4800(1.03) x Determine the value of the investment after 4 years. A. $ B. $ C. $ D. $ Indira invested $1500 at 2%/a compounded semi-annually. Define an exponential growth function for this investment in the form A(n) = P(1 + i) n where n represents the number of compounding periods. A. A(n) = 1500(1.01) n B. A(n) = 1500(1.04) n C. A(n) = 2500(1.02) n D. A(n) = 2500(1.002) n 34. Solve the following investment equation for the number of compounding periods, n. Round your answer to the nearest whole number. 350 = 300(1.04) n A. 2 B. 4 C. 8 D Solve the following investment equation for the number of compounding periods, n. Round your answer to the nearest whole number. 500 = 450(1.003) n A. 25 B. 30 C. 35 D Denis recently spent $1280 on a new laptop for his home business. He read that the depreciation rate for this model laptop is 25%. How much money should Denis expect to sell his laptop for in three years? A. $540 B. $960 C. $320 D. $740 Short Answer 1. Complete the table of values for the function f(x) = 2 x. x f(x) June

7 2. Complete the table of values for the function g(x) =. x g(x) 3. Determine if the data in the table represents an exponential function. Provide your reasoning. x y Determine the y-intercept of the exponential function f(x) =. 5. Determine if the exponential function f(x) = is increasing or decreasing. 6. Determine if the exponential function g(x) = is increasing or decreasing. 7. Solve the following exponential equation by writing both sides with the same base. 8. Solve the following exponential equation by writing both sides with the same base. 9. Solve the following exponential equation by writing both sides with the same base. 10. Solve the following exponential equation. 11. A research lab has a 12 mg sample of a radioactive substance. The amount of the substance, A(t), left in the sample can be modelled by the half-life function where t represents the time, in days, after the initial time. How long does it take for the sample to reduce to one quarter its initial amount? 12. A research lab has a 12 mg sample of a radioactive substance. The amount of the substance, A(t), left in the sample can be modelled by the half-life function where t represents the time, in days, after the initial time. What percent of the original sample will remain after 10 days, to the nearest whole number? 13. Determine whether the following data set involves exponential growth, exponential decay, or neither. Explain how you know. x y June

8 14. Determine whether the following data set involves exponential growth, exponential decay, or neither. Explain how you know. x y The number of bees in a colony is modelled by the equation N(d) = 120(1.15) d where N(d) represents the number of bees and d represents the number of days from now. How many bees should the beekeeper expect after a week? 16. The fish population in Loon Lake is modelled by the equation P(t) = 2500(0.92) t where P(t) represents the number of fish and t represents the time, in years, since Estimate the fish population in How long, to the nearest tenth of a year, does it take for the value of an investment to double when it earns 6%/a? 18. Nevia invested $3000 at 1.3%/a compounded weekly. Define an exponential growth function for this investment in the form A(n) = P(1 + i) n where n represents the number of compounding periods. 19. Pavendeep recently spent $ on a new car. He read that the depreciation rate for this model of car is 14%. How much money is Pavendeep s car worth in 6 years? 20. Amanda inherited a set of rare silver coins from her grandfather. An appraiser told Amanda that the coins are currently worth $850 and their appreciation rate will likely be 2.8%. How long, in years from the time of the appraisal, will it take for the coins to be worth $1000? Problem 1. Which exponential function matches each graph below? Provide your reasoning. i) iii) ii) iv) a) b) 2. A vehicle was purchased for $ in The book value of the vehicle can be modelled by the exponential function where y represents the value in dollars and x represents the time, in years, after a) How does the value of the vehicle change over time? Explain how you know. b) Estimate the value of the vehicle in Show your work. June

9 3. The population of a town can be modelled by the exponential equation where y represents the number of people and x represents the time, in years, after a) Is the population of the town increasing or decreasing? Explain how you know. b) What does the constant term represent? Explain how you know. c) Estimate the population of the town in Show your work. 4. Use what you know about the exponential function to predict the number of x-intercepts, the y-intercept, the end behaviour, the domain, and the range of the following function: 5. Solve the equation and verify your answer by substitution. Show your work. 6. Solve the equation and verify your answer by substitution. Show your work. 7. Solve the equation and verify your answer by substitution. Show your work. 8. Solve the equation and verify your answer by substitution. Show your work. 9. The number of yeast cells in a sample is modelled by the function where N(t) represents the number of yeast cells and t represents the time, in hours. a) Determine the number of yeast cells after 12 hours. Show your work. b) Determine the number of yeast cells after 50 hours, to the nearest thousand cells. Show your work. 10. Thorium-227 has a half-life of 18.4 days. The remaining amount of a 50-mg sample of thorium-227 can be modelled by the equation where A(t) is the amount of thorium-227 remaining, in milligrams, and t is the time in days. a) Determine the amount of thorium-227 remaining after 10 days, to the nearest milligram. Show your work. b) Determine the amount of thorium-227 remaining after 100 days, to the nearest tenth of a milligram. Show your work. 11. The number of yeast cells in a sample is modelled by the function where N(t) represents the number of yeast cells and t represents the time, in hours. a) Determine when there are 8000 yeast cells. Show your work. b) Use a graphing calculator to determine when there are yeast cells, to the nearest tenth of an hour. Show your work. June

10 12. Thorium-227 has a half-life of 18.4 days. The remaining amount of a 50-mg sample of thorium-227 can be modelled by the equation where A(t) is the amount of thorium-227 remaining, in milligrams, and t is the time in days. a) Determine when 12.5 mg of thorium-227 are remaining. Show your work. b) Use a graphing calculator to determine when 5 mg of thorium-227 are remaining, to the nearest day. Show your work. 13. The population of a town has been growing exponentially. The data table shows the town population in thousands over a 50 year period. Year Population (thousands) a) Use exponential regression to model the population growth. Round all values to the nearest hundredth. b) Estimate the population of the town in 1950, to the nearest hundred people. Show your work. c) Estimate the population of the town in 2030, to the nearest hundred people. Show your work. June