LESSON
Review
Exponents & Logarithms
Identify whether the following is growth or decay, the values for a and b and the y intercept.
1. j(x) ’ −2(0.5)x 2. p(x) ’ 4(1.4)x
Solve.
3. A certain car depreciates about 15% each year.
a. Write a function to model the depreciation
in value for a car valued at $20,000.
b. Graph the function.
c. Suppose the car was worth $20,000 in 2005.
What is the first year that the value of this car
will be worth less than half of that value?
Identify the inverse of the following functions.
4. f (x ) ’ 5x + 2 5. f (x ) ’ x + 6 6. [pic]
7. [pic] 8. [pic] 9. [pic]
Graph each function. Then write and graph its inverse.
10. f (x ) ’ 2x − 4 11. [pic]
Write each exponential equation in logarithmic form.
12. 3 7 ’ 2187 13. 12 2 ’ 144 14. 5 3 ’ 125
Write each logarithmic equation in exponential form.
15. log10 100,000 ’ 5 16. log4 1024 ’ 5 17. log9 729 ’ 3
Evaluate by using mental math.
18. log 1,000,000 19. log 10 20. log 1
Use the given x-values to graph each function. Then graph its inverse. Describe the domain and range of the inverse function.
21. f (x ) ’ 2 x ; x ’ −2, −1, 0, 1, 2, 3, 4
Express as a single logarithm. Simplify, if possible.
22. log6 8 + log6 27 23. log3 6 + log3 13.5 24. log4 32 + log4 128
25. log2 1920 − log2 30 26. log3 486 − log3 2 27. log6 180 − log6 5
Simplify, if possible.
28. log4 16 29. log2 8 x+12 30. [pic]
Solve.
31. 35x ’ 272x + 1 32. 36x + 2 ’ 64x 33. 55x - 6 ’ 50
34. 163x ’ 64x + 9 35. 81x ’ 243x + 2 36. [pic]
37. log x − log 9 ’3 38. log x + log 4 ’1 39. log (x + 6) ’ log(5x − 2)
Solve.
40. Halle deposited $4000 into an account that earns 5% interest each year. The
growth of her investment can be expressed by the exponential equation
A ’ 4000 (1 + 0.05)t, where A is the amount in the account after t years. In how
many years will her account exceed $10,000?
From the question above – what is the amount Halle will have, after the same number of years if the compounding is:
a. Quarterly
b. Daily
c. Continuous
Write each transformed function.
41. The function f (x) ’ log x is reflected across the y-axis.
42. The function f (x) ’ 8x is vertically stretched by
a factor of 2.
43. The function f (x) ’ 3x is moved left 4 units and two units down.
44. The function f (x) ’ ln x is shifted 3 units right and reflected
across the x-axis.
a. Write the function that is shifted 3 units right.
b. Take your answer to part a and write a function that
reflects it across the x-axis.
Given the parent function f(x) = 2x : state the transformation, the y intercept and the asymptote of the new function.
45. g(x) = 2x – 3
46. g(x) = 2x+4
47. g(x) = -3*2x
Given the parent function f(x) = log x : state the transformation and the asymptote of the new function.
48. g(x) = log x + 2
49. g(x) = log (x+2)
50. g(x) = -3*log x
Simplify.
51. ln ex + 2 52. eln 2x 53. e7 ln x
54. ln e3x + 1 55. ln e 56. ln e2x + y
Solve.
57. Use the formula A ’ P ert to compute the total amount for an investment
of $4500 at 5% interest compounded continuously for 6 years.
Answers:
1. Decay, a= - 2 , b = .5 , y intercept = - 2
2. Growth, a = 4 , b = 1.4 , y intercept = 4
3. a. y ’ 20,000( 0.85)x
b. [pic]
c. 2010
4. f −1(x) ’ [pic] 5. f −1(x) ’ x − 6 6. f −1(x) ’ [pic]
7. f −1(x) ’ −12x 8. f −1(x) ’ 4x +12
9. [pic], or [pic]
10. [pic]
[pic]
11. [pic]
[pic]
12. log3 2187 ’ 7 13. log12 144 ’ 2 14. log5 125 ’ 3
15. 105 ’ 100,000 16. 45 ’ 1024 17. 93 ’ 729
18. 6 19. 1 20. 0
21. Domain: {x|x > 0}; range: all real numbers
[pic]
22. log6 216 ’ 3 23. log3 81 ’ 4 24. log4 4096 ’ 6
25. log2 64 ’ 6 26. log3 243 ’ 5 27. log6 36 ’ 2
28. 0 29. 3x + 36 30. 30
31. x ’ −3 32. x ’ 2 33. x ( 1.686
34. x ’ 9 35. x ’ −10 36. x ’ −2
37. x ’ 9000 38. x ’ 2.5 39. x ’ 2
40. 19 years
a. $10282.11
b. $10322.45
c. $10342.84
41. g(x) ’ log (−x)
42. g(x) ’ 2(8)x
43. g(x) ’ 3x+4 - 2
44. a. g(x) ’ ln (x - 3)
b. g(x) ’ −ln (x - 3)
45. Down 3, -2, -3
46. Left 4, 16, 0
47. Reflected across x & Vert Stretch by 3, -3, 0
48. Up 2, 0
49. Left 2, -2
50. Reflected across x & Vert Stretch by 3, 0
51. x + 2 52. 2x 53. x7
54. 3x + 1 55. 1 56. 2x + y
57. $6074.36
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- water theme preschool lesson plans
- lesson plans high school history
- lesson plans for us history
- lesson plans for kindergarten
- lesson plan themes by month
- preschool lesson on water
- water lesson plan for preschoolers
- living water lesson for kids
- free printable english lesson worksheets
- water lesson plans for toddlers
- free lesson plans for english
- water lesson plans pre k