1. CHAPTER 5 REVIEW Exponential and Logarithmic Functions

2. Directions You need a piece of paper (or dry erase board), a pencil (or marker), & a calculator. You need a piece of paper (or dry erase board), a pencil (or marker), & a calculator. We will go through a series of review problems, solving them and then reviewing them as a class. Each slide will take 1 to 2 minutes. We will go through a series of review problems, solving them and then reviewing them as a class. Each slide will take 1 to 2 minutes.

3. 1 Evaluate a. log (100) = b. log 5 5 7 = c. log 18 9 18 = 2 7 1/9

4. 2 Solve (nearest 100 th ) a. 7 x = 343 b. 12 a+1 = 1000 c. (0.4) w = e x = 3 a = 1.78 w = -1.09

5. 3 Solve. Nearest Hundredth a. log x = 2.91 b. 2 ln 15 = ln x c. log x 64 = 3 x = 812.83 x = 225 x = 4

6. 4 (evaluate) a. log 97, 234 = b. ln 10 = c. ln (-4.1) = 4.99 2.30 undefined! W H Y ?

7. 5 For the graph of f(x) = e x a. Give the domain. b. Give the range. c. Name the asymptote(s). All reals Positive reals x - axis

8. 6 Given y = ab x When is the equation a. growth? b. decay? when b > 1 when 0< b < 1

9. 7 Write in exponential form: a. ln (6.28) = 1.8 b. log 6 = -3 1 216 e 1.8 = 6.28 6 -3 = 1 216

10. 8 Strontium 90 has a half-life of 29 years. How much will be left of 5 grams after 116 years? y = 5 (.5 ) (116/29) = 0.3125 grams

11. 9 Rewrite as the log of a single quantity. a. log x – log y b. 2 ln 5 + ln 10 c. 3 log 2 – log 4 log x y ln 250 log 2

12. 10 A new car costing $13,000 is predicted to depreciate at a rate of 12% per year. How much will the car be worth in 7 years? 13,000 (.88) 7 = $5,312. 78

13. 11 The population of a strain of bacteria grows according to N = N o (3) 0.827t where t is the time in hours. How long will it take for 30 bacteria to increase to 500 bacteria? 3.10 hours

14. 12 Consider y = 2 x and y = 5 x. a. Name three things the graphs have in common. b. Which graph is growing more quickly? How do you know? same y-intercept: (0, 1), exponential growths, x-axis is asymptote y = 5 x because 5 > 2

15. Tonight…… STUDY!!!!! R E M E M B E R …. There will be a non-calculator part to the test!