Welcome! The Topic For Today Is…

1. Welcome! The Topic For Today Is…

2. Exponential and Logarithmic Equations

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

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

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

6. Daily Double 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 Back

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. Back

9. Logarithmic Functions: 200 • Question: Write as a exponential equation. log381 = 4. • Answer 34 = 81 Back

10. Logarithmic Functions: 400 • Question: Solve the equation for x. log662 = x • Answer x = 2 Back

11. Logarithmic Functions: 600 • Question: Describe the relationship between thegraphs of f and g. f(x) = 5xg(x) = log5x • Answer The graphs are symmetric around the line y = x because f(x) and g(x) are inverse functions. Back

12. Logarithmic Functions: 800 • Question: Find the domain, range, vertical asymptote, and x- and y-intercepts of f(x) = 4 log5(x + 2) - 3 • Answer • Domain: (0, ∞) • Range: (- ∞, ∞) • Vertical Asymptote: x = -2 • x – intercept: ( 53/4 - 2, 0) • y – intercept: (0, 4 log52 – 3) Back

13. Logarithmic Functions: 1000 • Question: Graph f(x) = –log2(x - 4) + 5 • Answer See the teacher for the answer. Back

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

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

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

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

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

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

20. Daily Double 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 Back

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

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

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

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

26. Solving Equations: 400 • Question: Solve e2x – 4ex – 5 = 0. Round to 3 decimal places. • Answer ln5≈1.609 Back

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

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

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