1. PreCalculus 3-4 Solving Exponential and Logarithm Equations

2. Exponential & Log Equations

4. Find the solution to the equation, correct to three decimal places x=-1.535

5. Exponential & Log Equations

6. Solve the following equation, correct to three decimal places x=0.549

7. Exponential & Log Equations

9. Solve the equation. x=1.951

10. Exponential & Log Equations

11. Solve the equation. x=0.693

12. Exponential & Log Equations

13. Solve the equation. x=0 x=5

14. Exponential & Log Equations

17. Solve the equations x=20.086 x=14

18. Exponential & Log Equations

19. Solve the equation x=16666.667

20. Exponential & Log Equations

22. Solve the equation x=2

23. Exponential & Log Equations Solve the equation x=1001

24. Exponential & Log Equations

25. Solve the equation graphically x=-3.101 x=5.997

26. Exponential & Log Equations

28. Recall

29. Exponential & Log Equations

33. Exploration How long is it going to take to double my money?

34. Consider an investment of $100 invested at 5%, compounded continuously. How long would it take for the investor to have $200? How long is it going to take to double my money?

35. What would the doubling time be if the initial investment were $1,000? $10,000? What effect does changing the principal have on the doubling time, and why? How long is it going to take to double my money? The doubling time is not affected by changes in principal. Algebraically, the P o drops out of the exponential growth equation. Intuitively, the doubling time is a property of the ratio of two numbers, not a property of the numbers themselves.

36. One of the first things that is taught in an economics class is the Rule of 72. It can be summarized: "The number of years it takes an investment to double is equal to 72 divided by the annual percentage interest rate." How long is it going to take to double my money?

37. What would the Rule of 72 say the doubling time of a 5% investment is? Is it a good estimate? How long is it going to take to double my money? 14.4 years 3.87% error

38. Repeat for an investment of $100 at an interest rate of 3%, 8%, 12% and 18%. What can you say about the accuracy of the Rule of 72? How long is it going to take to double my money? Interest RateActual Doubling TimeEstimated Doubling Time Error 3%23.1 years24 years3.90% 8%8.66 years9 years3.92% 12%5.78 years6 years3.81% 18%3.85 years4 years3.90%

39. Derive a precise formula for the time T to double an initial investment. How long is it going to take to double my money?

40. There is an integer that gives a more accurate answer for continuous or nearly continuous compounding than the Rule of 72. What is this number? Check your answer by using it to estimate the doubling time of a 5% investment. How long is it going to take to double my money? 69 13.8 years 0.4% error

41. It turns out that there is a reason that we use the number 72 in the Rule. It has to do with one of the assumptions we made. Why do economists use the Rule of 72? How long is it going to take to double my money? If the compounding is assumed to be annual, 72 works best for values of r between 3% and 15%. For example, 10% compounded annually doubles every 7.2735 years. The rule of 72 gives 7.2, a good approximation, and the rule of 69 gives 6.9, a bad one.

42. Exponential & Log Equations Homework pg. 213 - 215 18, 24, 28, 32, 34, 38, 48, 50, 52, 58, 76, 80, 82, 84, 103, 106, 109, 110, 112, 115, 121