Chapter 4
23. Graph each function. Is it exponential growth or decay?
1
a) y  4 x
b) y  2 0.5  x
2
1
24. The graph of f  x   2 x is transformed to g x  
 2  x  4 . Describe g as a transformation of f.
5
2x 1
25. Find the inverse of f x  
.
3
26. Graph f ( x)  3 x and its inverse function. Describe the domain and range of the inverse function.
1
27
27. Evaluate.
a) log 5 125
b) log 3
28. Simplify.
a) ln e 8
b) e ln 2 x
c) 5 log 5 4 x
d) log 4 4 6
29. Write log 3 8 as the quotient of two common (base 10) logs.
30. Express log 3 486  log 3 2 as a single logarithm and simplify.
31. Simplify log 5 x 4  log 5 x 2 . Express the answer in terms of log 5 x.
32. Solve for x. (round answers to parts c) and d) to the nearest hundredth)
a) log 3 x 2  log 3 2  3
b) 9 1 4 x  27 x 1
c) 2 x  5  18
d) e 2 x  45
33. The epidemic began with 30 persons infected. The number of infected persons increased by 47% each day after the
epidemic began.
a) Write a growth function in the form p  x   a  1  r  x that represents the total number of persons infected
after x days.
b) To the nearest day, about how many days did it take for 3,000 persons to become infected?
34. A car’s value decreases by about 15% per year. The original value of a brand-new car is $20,000.
a) Write a decay function in the form V x   a 1  r  x that represents the value of the car after x years.
b) To the nearest dollar, what is the car’s value after 3 years?
c) To the nearest tenth of a year, when will the car’s value be less than half of its original value?
35. Mayra invests $60,000 in a retirement account that earns 4.5 % compounded continuously. To the nearest dollar, what
is the total amount of her investment after 10 years? Use the formula A  Pe rt .
36. The Richter magnitude R of an earthquake is given by the model R = 0.67 log (0.37E) + 1.46,
where E is the energy (in kilowatt-hours) released by the earthquake. Suppose an earthquake releases
15,500,000,000 kwh of energy. What is the earthquake’s magnitude?
Chapter 5
37. If y varies inversely as x, write an inverse variation function if y = 250 when x = 6.
38. Simplify
 3x 2  8 x  3
x 2  6x  9
. For what value(s) of x is the expression undefined?
39. Divide:
4x3 y 2
2
2x  6x  4

12 x y
3 x 2  12
. Assume all expressions are defined.
x
18

. For what value(s) of x is the expression undefined?
2
x3 x  9
x5
6

41. Simplify:
. For what value(s) of x is the expression undefined?
2
x4
x  4 x  32
40. Simplify:
x
x 1
42. Simplify:
. Assume that all expressions are defined.
x
x
3
43. Solve for x.
a)
44. For g x  
1
 2,
x5
2 x 2  7 x  15
 10
2x  3
b)
a) describe g  x  as a transformation of the parent function f x  
b) identify the asymptotes of g  x 
c) identify the domain and range of g  x 
x
x
6x
 
x  3 2 2x  6
1
x