Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name______________________________ Algebra II 7.2 - 7.3 Worksheet Show all work for full credit! Date ______________________Hour ____ In #1 – 6, tell whether the function represents exponential growth or exponential decay. 74 x 87 x 1. f ( x) 2 2. f ( x) 3 3. f ( x) 130.34 x 4. f ( x ) 53 4 x 5. f ( x ) 13 e x 6. f ( x ) 8e x In # 7 – 11, graph each function without a calculator. Include 5 ordered pairs in each table. Give the domain and range. Give the equation for the horizontal asymptote. 7. f ( x) 15 x x y Domain: Range: Asymptote: 8. f ( x) 14 x x y Domain: Range: Asymptote: 15 x 9. f ( x) 2 x y Domain: Range: Asymptote: 10. f ( x) 13 x 1 x y Domain: Range: Asymptote: 11. f ( x) 2 14 1 x x y Domain: Range: Asymptote: 12. What is an asymptote of the graph of y A) y 3 13 x3 5 ? B) y 3 13. What is an asymptote of the graph of y 12 x 2 A) y 3 B) y 2 C) y 5 D) y 5 C) y 2 D) y 3 3? 14. You invest $500 in the stock of a company. The value of the stock decreases 2% each year. Describe and correct the error in writing the a model for the value of the stock after t years. y initial amount Decay factor t y 500 0.02 t 15. You invest $600 in the stock of a company. The value of the stock decreases 3.5% each year. a) Write a model for the value of the stock after x years. b) Find the value of the stock after 7 years. 16. You buy a new car for $28,999. The value of the car decreases by 16% each year. a) Write an exponential decay model giving the car’s value (in dollars) after x years. b) What is the value of the car after 5 years? 17. You buy a new mountain bike for $200. The value of the bike decreases by 25% each year. a) Write a model giving the bikes value y (in dollars) after t years. b) What is the value of the bike after 3 years? 18. When a plant or animal dies, it stops acquiring carbon-14 from the atmosphere. Carbon-14 decays over time with a half life of about 5730 years. The percent P of the original amount of carbon-14 that remains in a sample after t years is given by the equation below. What percent of the original carbon-14 remains in a sample after 2500 years? 19. The number of E of eggs a leghorn chicken produces per year can be modeled by the equation E 179.20.89 w 52 where w is the age (in weeks) of the chicken and w 22. Estimate the egg production of a chicken that is 2.5 years old. In # 20 – 27, simplify each (no calculator). 3 20. e5 e 4 21. e 7 e 2 22. 3e 2 5e 3 23. 2e 5 x 24. 2e 25. 5e 26. e x e 5 x e 3 27. e x 8e x 5 6 4 27e 9 x ? 3e 5 x 7 28. What is the simplified form of A) 9 2 e4 x8 6 x 1 2 4 B) 3e x 4 8 C) 3e x D) 9 2 e2 x 4 In # 29 – 32, use a calculator (nearest hundredth) to evaluate each expression. 29. e5 30. e 7 2 31. 12e 5 3 2.4 32. 9e 33. The number of camera phones shipped globally can be modeled by the function y 1.37e where x is the number of years since 1998 and y is the number of camera phones shipped (in millions). How many camera phones were shipped in 2006? 1.43 x 34. Scientists used traps to study subterranean termite populations in New Orleans. The mean number of y termites collected annually can be modeled by y 728e number of termites collected in 2000? 0.329t where t is the number of years since 1986. What is the mean 35. You deposit $3500 in an account that pays 3% annual interest compounded continuously. What is the balance after 5 years? 36. In 2009, you deposit $12,000 in an account that pays 2.35% annual interest compounded continuously. What is the balance in 2013?