Algebra 2
Chapter 7 Test Review 2
Determine whether the following functions are exponential growth or decay functions. Explain.
x
x
x
1
x
1 7
x 1
4
2
1) y   
2) y  4 
3) y  3  
4) y  4  
5) y   4 
6
3 4 
5
3
Rewrite in exponential form.
6) log 4 16  2
1
7) log 2    3
8
Rewrite in logarithmic form.
5
1
2
10) 7  49
11)    32
2
Evaluate WITHOUT using a calculator:
14) log 3 27
15) log 7 1
8) ln 3  1.099
9) ln 1  0
12) 103  1000
13) e 3  .0498
16) log 4
1
16
17) log 5 125
Use properties of logs to rewrite the expression in terms of log 5 2, log 5 3, or log 5 7
18) log 5 14
19) log 5 49
Expand completely. Simplify if possible:
22) log 3 81x 5 yz 4
Condense:
20) log 5 6
23) ln
21) log5
21
2
73 x
10 y 4 z 2
1
ln x  5  2 ln x  ln y
2
24) 2 log x  3log y  log z
25)
Evaluate. Round to the nearest thousandth.
26) log 7 120
27) log15 10
Condense and simplify. Show all work.
28) log 3 12  2log 3 2
29) log 6 24  2log 6 3
Solve. Remember to check for extraneous solutions!
Round to the nearest thousandth if needed.
1
64
30) 91 x  27 2 x 14
31) 16 x 
32) log 4 ( x  1)  log 4 ( x  3)  log 4 15
33) log x 2  2
34) log 2 ( x  1)  log 2 ( x  1)  4
35) 4 log 3 x  log 3 3  3
36) 2e  x  1  15
37) 12 x 1  7
38) ln  x  2 2  2
39) ln 9 x  ln x  4
y  a1  r 
t
 r
A  P 1  
 n
nt
A  Pe rt
y  ae kt
40) You deposit $1200 in an account that pays 5% annual interest. After 10 years, you withdraw
the money. Find the balance in the account if the interest is compounded
a) Quarterly
b) Weekly
c) Continuously
41) The current ticket price at the Starplex Cinemas at the East Brunswick Square Mall is $8.50. If
ticket prices increase each year by 2.5%, how much will ticket prices cost in 5 years?
42) The population of Bearsville 10 years ago was 150,000. Since then, the population has
increased at a steady rate each year. The population is currently 185,000.
a. Write an exponential function that could be used to model the population after t years.
b. What will the population of Bearsville be in 25 years?
43) An equation that models the decline in the number of US farms is y  3,962,000 e .02t , where t is
the number of years since 1960 and y is the number of farms.
a. How can you tell that the number is declining?
b. What was the number of US farms in 1960? Explain how you found this number.
c. Predict when the number of farms will be less than 1 million.
44) Identify the following information for the function: f  x   3  1 
 
a) Domain: _____________________
b) Growth or decay?
____________________
c) y-intercept:
___________________________
2
x 1
5
d) Range: __________________________
e) Asymptote: ______________________
f)
Transformations from the parent
function:
45) Given the graph of the exponential function, identify the asymptote, domain, and range:
a) Asymptote: ___________________
b) Domain:______________________
c) Range:________________________
d) y-intercept:_________________________
e) Type of Exponential: _________________
46) No Calculator: Graph and state all key features. f ( x )  3(2) x  2  1
Type of Graph: _____________
Domain: ___________________
Range: ____________________
Asymptote: ________________
y-intercept: ________________
Transformations:
End Behavior: