7.2 Review Worksheet (continued)
7.2.2 The Natural Base, e Graph. 17. f ( x ) = e x + 1
18. f ( x ) = e x − 1
19. f ( x ) = 1 − e x
20. f ( x ) = 10 − e x
Simplify. 21. ln e 0
22. ln e 2 a
23. e ln( e + 2)
24. e 4ln x
25. Aidan has $7565 in his checking account. He invests $5000 of it in an account that earns 3.5% interest compounded continuously. What is the total amount of his investment after 3 years?
26. An accident in 1986 at the Chernobyl nuclear plant in Ukraine released a large amount of plutonium (Pu-239) into the atmosphere. The half-life of Pu-239 is about 24,110 years. Find the decay constant. Use the function N ( t ) = N 0 e − kt to find what remains of an initial 20 grams of Pu-239 after 5000 years. How long will it take for these 20 grams to decay to 1 gram?
7.2.3 Transforming Exponential and Logarithmic Functions Make a table of values, and graph each function. Describe the asymptote. Tell how the graph is transformed from the graph of f ( x ) = 5 x . 27. g ( x ) = 5 x − 1 28. h ( x ) = 5 x + 2 29. j ( x ) = 5 x + 1 − 1
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