Answers to Chapter Test Forms 1
CHAPTER 4, FORM D
COLLEGE ALGEBRA
NAME
DATE
1. Consider the function defined by
( )
321f x x=−
.
a. What are the domain and range of f? 1a._______________________________
b. Find the rule for
( )
1
fx
–
. 1b._______________________________
c. What are the domain and the range of
1
f–
? 1c._______________________________
2. Match the equation with its correct graph:
2x
y–
=
2. _______________________________
(a) (b)
(c)
(d)
Graph the function.
3.
31
x
y–
=+
3.
4. Solve
2 1 2
3 27
xx–=
. 4._______________________________
5a. Write
12
77=
in logarithmic form. 5a._______________________________
5b. Write
3
49
1
log 7 6
=
in exponential form. 5b._______________________________
Answers to Chapter Test Forms 2
CHAPTER 4, FORM D
6. Use properties of logarithms to write the following 6._______________________________
as a sum, difference, or product of logarithms.
22
3
log xz
y
Use a calculator to find approximations for each of the following logarithms. Express answers to three decimal
places.
7. ln 897 7._______________________________
8. ln a = –2.9 8._______________________________
9.
1.9
log 25.6
9._______________________________
10. If
() x
f x a=
and
(3) 1000,f=
find the following values of
( ).fx
a. f (2) 10. a._______________________________
b. f (0) b._______________________________
11. What values of x cannot possibly be solutions of 11._______________________________
the following equation?
log (2 3) 2
ax– = –
Use properties of logarithms to solve each equation. Express answers to three decimal places.
12.
2log log(6 )xx=-
12._______________________________
13.
99
log log ( 8) 1xx+ – =
13._______________________________
14.
3
log (4 5) 4m+=
14._______________________________
15.
3 3 3
log 6 log (2 3) log ( 1)xx– + = +
15._______________________________
16. Between what two consecutive integers must x be 16._______________________________
if
5 50
x=
? Explain why this is so. _______________________________
17. The population of Twin Lakes is given by the function
.02
( ) 3250 ,
x
P x e=
where x is the number of years after 1970.
a. What will the population be in the year 2015? 17. a._______________________________
b. In what year will the population of Twin Lakes b._______________________________
be double the population of 1970?
18. The temperature of a liquid t minutes after being 18._______________________________
placed into an environment having constant
Answers to Chapter Test Forms 3
temperature
0
T
is given by
.12
0
( ) 100 .
t
T t T e–
=+
How long, to the nearest minute, will it take a mug of
hot chocolate to cool to a temperature of 25°C in a
room at 15°C?
CHAPTER 4, FORM D
19. How many years, to the nearest tenth, will be needed 19._______________________________
for $5000 to increase to $8,000 at 3% compounded
monthly?
20. The population of a town is 1900 and increasing at a 20._______________________________
rate of 1.4% per year, while the number of dogs in the
town is currently 650 and increasing at a rate of 8% per
year. Assuming this trend continues, estimate graphically
when the dog population will exceed the human
population in this town.
Answers to Chapter Test Forms 4
CHAPTER 4, FORM D
Answers to Chapter Test Forms 5