Precalculus Review Worksheet for First Chapter 5 Test ______

Precalculus Review Worksheet for second Chapter 4 test ______name For the test, you must know the exponential growth equations. They will not be provided for you. Very specific formulas, like Newton’s law of cooling, will be provided. t a. A (t) = A (1 + r)t b. A (t) = A c. A (t) = A ert 0 0 b k 0

a You also must know the laws of logarithms. They will not be provided to you. Remember logbx = a IFF b = x log c ln c log c M k a d. log b MN = log b M + log b N e. log b = log b M  log b N f. log b M = k log b M g. log bc =   N log b ln b log a b

The test will have 2 pages. On the first page, you will not be able to use a calculator. On the second, you will. I. Simplify the following expressions, if possible. Answers to log problems should be exact - either in fractional or radical form. Get the answer w/out a calculator!

3 1. log 1000 2. log .001 3. log 3 81 4. log 5 .04 5. log 7 ( 7 7 )

2 1 6. ln e 7. ln 8. log 5 2 + log 5 3 9. log 3 + log 6  log 2 e3

1 1 10. ln 25  ln 2 11. 2 log P  log Q 12. log b M + log b N  3 log b P 13. ln c + ln d 2 3

14. ln e3 15. ln e5y 16. 10log 6 17. 10 2+logx 18. 10 4log2

log 32 3 100 8 4 19. log3 81 20. log(log 100 ) *21. log4(log22 ) *22. *23. If logbM = 3, then logMb = ? log8 16

II. Solve for x. Try not to use a calculator. Leave answers in exact form. 24. log x = 5 25. x3 = 20 26. log | x | = 2 27. ln ( ln x ) = 2

3 x+1 2x 28. log 5 ( log 4 x ) = 0 29. log 3 ( log 5 x ) = 1 30. (log x) = 27 31. 3 = 6

(*problems taken from math team competitions) 2 32. log 5 x + log 5(x  4) = 1 33. log 3( x + 1 ) + log 312 = 4 34. log 9 (x + 12) = log 9 x + log 9 7

35. log (3x  1)  log (2x + 5) = 2 36. 32x  11  3x  12 = 0 37. e2x  8ex + 15 = 0

38. 3x = 26 39. e x = 70 40. 52x = 100

III. Solve the following word problems 41. An investment is made at 5.75% compounded quarterly. How long does it take to double the investment?

42. If an investment of $1000 is compounded continuously, what interest rate must you get to triple the money in 12 years? (round to hundredth of a percent)

43. Uranium 238 has a half life of 4.5 billion years (!!). How long will it take 1 kg to decay to 1 g?

44. How long does it take $500 to become $2000 if it is invested at 3.25% and compounded a) yearly b) continuously ?

I 45. Decibel Level is found by using this formula dB = 10 log . What is the decibel level of 3 stereos, each playing at 72 dB? I 0

46. The population of a certain country was 2,345,235 in 1985 and 3,458,377 in 1995. Assume that the growth is exponential. (a) Find a formula for the population t years after 1985. (b) Find the time required for the population to double. (b) Use the data to predict the population in the year 2005.

47. A kettle full of water is brought to a boil in a room with temperature 32° C. After 5 minutes the temperature of the water has decreased from 100° C to 80°C. Find the temperature after another 5 minutes.

48. A substance has a hydrogen ion concentration of [ H+ ] = 2.1 * 10-2 M. Find the pH of the substance.