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2. Exponential and Logarithmic Equations Exponential Functions Logarithmic Functions Expanding Expressions Condensing Expressions Solving Equations 200 400 600 800 1000

3. Exponential Functions: 200 Question: Evaluate f(x) = 25 -3x at x=2/3. Answer 0.0016 or 1/625

4. Exponential Functions: 400 Question: What is the asymptote of f(x) = 0.3 x+1 ? Answer y = 0

5. Exponential Functions: 600 Question: Is the function increasing or decreasing? g(x) = 0.3 -x Answer Decreasing

6. The Winner Of The Last Round Write Down How Much Money You Are Willing To Risk If You get the Question write you win that money If you get it wrong you Loss the money!

7. Exponential Functions: 800 Question: A car is bought for $24,000. It depreciates at a rate of 14.5% per year. What will the value of the car be in 10 years? Answer $5010.40

8. Exponential Functions: 1000 Question: There are 3 options for investing $500. The first earns 7.5% compounded annually, the second earns 7.25% compounded quarterly, and the second earns 7% compounded continuously. Determine which investment yields the highest return in 20 years. Answer Option Number 1.

9. Logarithmic Functions: 200 Question: Write as a exponential equation. log 3 81 = 4. Answer 3 4 = 81

10. Logarithmic Functions: 400 Question: Solve the equation for x. log 6 6 2 = x Answer x = 2

11. Logarithmic Functions: 600 Question: Describe the relationship between the graphs of f and g. f(x) = 5 x g(x) = log 5 x Answer The graphs are symmetric around the line y = x because f(x) and g(x) are inverse functions.

12. Logarithmic Functions: 800 Question: Find the domain, range, vertical asymptote, and x- and y-intercepts of f(x) = 4 log 5 (x + 2) - 3 Answer – Domain: (0, ∞) – Range: (- ∞, ∞) – Vertical Asymptote: x = -2 – x – intercept: ( 5 3/4 - 2, 0) – y – intercept: (0, 4 log 5 2 – 3)

13. Logarithmic Functions: 1000 Question: Graph f(x) = –log 2 (x - 4) + 5 Answer See the teacher for the answer.

14. Expanding Expressions: 200 Question: Expand the log. ln (z(z + 1) 2 ) Answer ln z + 2ln(z + 1)

15. Expanding Expressions: 400 Question: Expand the natural log. ln Answer

16. Expanding Expressions: 600 Question: Expand the natural log. Answer ln (x + 1) + ln (x – 1) – 3 ln x

17. Expanding Expressions: 800 Question: Expand the natural log. Answer 4 ln x + ln y – 5 ln z

18. Expanding Expressions: 1000 Question: Expand the log. Answer

19. Condensing Expressions: 200 Question: Condense the logarithm to a single quantity. 4[lnz + ln(z + 5)] – 2ln(z – 5) Answer

20. The Winner Of The Last Round Write Down How Much Money You Are Willing To Risk If You get the Question write you win that money If you get it wrong you Loss the money!

21. Condensing Expressions: 400 Question: Condense the logarithm to a single quantity. Answer

22. Condensing Expressions: 600 Question: Condense the logarithm to a single quantity. 2[ln x – ln(x + 1) – ln(x – 1)] Answer

23. Condensing Expressions: 800 Question: Condense the logarithm to a single quantity. Answer

24. Condensing Expressions: 1000 Question: Condense the logarithm to a single quantity. Answer:

25. Solving Equations: 200 Question: Solve ln(2x – 1) = 5. Round to the nearest hundredth. Answer

26. Solving Equations: 400 Question: Solve e 2x – 4e x – 5 = 0. Round to 3 decimal places. Answer ln5≈1.609

27. Solving Equations: 600 Question: Solve -2 + 2ln(3x) = 17. Round to 3 decimal places. Answer 4453.242

28. Solving Equations: 800 Question: Solve ln(x + 5) = ln(x – 1) – ln (x + 1) Answer No real solution.

29. Solving Equations: 1000 Question: Solve and round to 3 decimal places. Answer 180.384