Algebra 2 – Chapter 8 Test (Including Sections 7.6 and 7.7)
Graph the function.
Name:
Date:
Period:
Write an exponential function y  ab x for a
graph that includes the given points.
1) y  0.5(3) x
2) (1,12),(4,324)
Determine whether each function
represents exponential growth or
decay. State the percent increase or
decrease.
Find the amount in a continuously
compounded account for the given
conditions.
a ) y  6(1.4) x
3) b) y  0.2(0.72)
1
c ) y  2 .7  
5
x
Pr inicpal : $3600
4) Annual Interest : 2.15%
Time : 8 years
x
Write in logarithmic form.
Write in exponential form.
a) log 4 4096  6
a) 9 4  6561
5)
b) 2  4 
1
16
Evaluate each logarithm.
6)
b) log 6 1296  4
Graph the function.
a ) log 4 32
8) y  log 3 x
7)
b) log 9 243
Write each logarithmic expression
as a single logarithm.
Expand each logarithm.
9) a) log 16 – log 10 + log 3
10)
b) 10 log y + 5 log m -
c)
2
log n
3
a) log 7 x 4 y
b) log
c2d
4
e
1
2
log 144 + log 2 - log 8
2
3
Solve each equation. Round your answer to the nearest ten-thousandth.
11) 5 x  16
12) 7 x 3  89
13) 114 x 1  56
14) 2 6 x 3  17  44
Use the change of base formula to evaluate the expression. Then convert it to a logarithm
base 6.
15) log 4 15
Solve each equation. Round to the nearest hundredth, if necessary.
16) log 16 x  2
17) log (5 x  12)  3
Write the expression as a single natural logarithm.
19) 9 ln x + 5 ln 5 – (8 ln m + 4 ln y)
18) log 2 8x  log 2 3  5
Solve each equation. Round to the nearest hundredth.
20) ln 3x = 6
21) ln  x  1  3
2
22) ln
x7
=2
5
Use natural logs to solve each equation. Round to the nearest hundredth.
23) e
x2
 11
24) e
5 x 1
 21
x
6
25) e  18  52
Solve.
26) An initial deposit of $6300 is now worth $8073.20. The account earns 3.1% interest
and is compounded continuously. For how long has the money been in the account?
For #27 and #28, let f ( x)  x 2  3x  5 and g ( x)  5 x  12 .
27)
a) find: f ( x)  g ( x)
28) find: f ( x)  g ( x)
b) find: f ( x)  g ( x)
For #29 and #30, let f ( x)  4 x  5 and g ( x)  x 2  6 x  2
29) find: ( g  f )( x)
30) find: ( f  g )(3)
Graph each relation and its inverse.
31) y  2 x  4
32) y  ( x  1) 2  4
33) State the domain and range of the relation and its inverse in #32.
Bonus Problems (worth 1 point each)
34) If the parent function of an exponential function is f ( x)  6(4.2) x , write the equation
for this function if it were translated 4 units to the right and 11 units up.
Use the properties of logs to evaluate the expression.
35) log 4 8  2 log 4 4  log 4 2
Expand the logarithm.
36) log 5 14
x6 y
289
Use natural logarithms to solve the equation. Round to the nearest hundredth.
37) 8e
x
5
 19  27