MATH 1113
Review—Chapter 5
Complete each table and then graph the functions by plotting at least 3 points.
1. y  3 x
2. y  3(0.6) x
3. y  5(1.25) x
x y
-2
-1
0
1
2
x y
-2
-1
0
1
2
x y
-2
-1
0
1
2
Complete the following table.
Function
4.
5.
6.
7.
8.
9.
Initial value
(y-intercept)
Base
Growth or
Decay?
Rate of growth
or decay (%)
decay
growth
75%
100%
y  5(1.14) x
y  (0.9) x
y  100e 0.08 x
y  50e 0.6 x
8
10
10. At the end of an advertising campaign, weekly sales declined according to the equation
y  8000  2 0.04 x dollars, where x is the number of weeks after the campaign.
a) Determine the sales at the end of the campaign.
b) Determine the sales 6 weeks after the end of the campaign. (Round to the nearest cent.)
c) After how long will the sales be at $4000? (Round to the nearest week.)
11. If $5000 is invested for t years at 2% interest compounded continuously, the future value is
given by S  5000e 0.02t dollars.
a) Graph this function for 0  t  15 .
b) Determine the value of the investment after 10 years. (Round to the nearest cent.)
c) When will the future value be $20,000? (Round to the nearest year.)
12. The amount of a certain radioactive isotope present at time t is given by
A(t )  450e 0.0072t grams, where t is the time in years.
a) What is the initial quantity (at time 0)?
b) How many grams remain after 80 years? (Round to the nearest gram.)
c) Determine the half-life of this isotope (to the nearest year.)
Rewrite each logarithmic equation as an exponential equation and vice-versa.
13. log 27 (3) 
1
3
14. log 5 0.2  1
1
17. e  2 
16. 36 2  6
1
e2
15. log m p  r
18. g h  w
Rewrite each logarithmic equation as an exponential equation and solve for x.
19. log 25 x 
1
2
20. log 3 (5 x  7)  2
21. ln( 3 x  5)  0
Find the value of each logarithm without a calculator.
1
25
22. log 7 49
23. log 5
25. ln e 3
26. log 15 15
28. Given the graph of f ( x)  a x ,
sketch the graph of f 1 ( x)  log a x .
24. log 11 11
27. log 8 1
State the inverse function, f
29. f ( x)  ln x
1
( x) , for each of the following.
30. f ( x)  7 x
Expand each of the given logarithmic expressions into a sum, difference, and/or constant
multiple of logarithms. Expand and simplify as much as possible.
 10 x 
x y

31. log( x 3 y )
32. log 
33. ln  4 
 y
 e 


Write each expression as a single logarithm with coefficient 1.
34. log 5 ( x)  log 5 ( y)  log 5 z
35. 4 ln( x)  12 ln( y)
36. 2 log x  14 log y  5 log z
Use the change-of-base formula to find an approximation to four decimal places for each
logarithm.
3
37. log 5 8
38. log 2  
39. log 15 30
7
Solve each equation algebraically. Show your work! Give the exact answer as well as a
decimal approximation to the nearest thousandth.
40. log 6 (3x  5)  2
41. log 5 (4 x)  7  5
43. log 7 ( x  3)  log 7 (3x  5)  1
45. 5e x 3  20
46. 7  (1.5) x  3  17
42. log( 7)  log( x  1)  2
44. log 4 ( x  3)  log 4 x  1
47. 100e .06 x  300
48. Suppose a population starts out with 50,000 people, but it decreases by 2% each year.
a) Write an exponential function which models the size of the population at time t years.
b) What would the population be after 8 years?
c) How long will it take (to the nearest year) for the population to be reduced to 10,000?
49. Find the amount in an account (to the nearest cent) after 10 years if $1000 is invested at 3%
annual interest, compounded
a) annually
b) quarterly
c) monthly
d) weekly
e) daily
f) continuously
50. Suppose you want to have $25,000 in your bank account after 18 years. If you earn 2.5%
interest, compounded continuously, how much must you invest? (Round to the nearest
cent.)
51. How long (to the nearest year) will it take an investment to double if it earns 4%
compounded annually?
52. In some states, coastal property is increasing in value by 12% per year. Suppose a property
has an initial value of $250,000.
a) Write an exponential function modeling the property’s value after t years.
b) After how many years will the property be worth $1,000,000? (Round to the nearest
year.)