ALGEBRA II CHAPTER 6 PRACTICE TEST (SECTIONS 6.1 THROUGH 6.6)
Name_____Key______________________________
Period______
Date____________
Learning Target #27: I can create, graph, and evaluate exponential functions.
Learning Target #28: I can apply natural base e to exponential functions.
Graph the equation.
1.
𝑦 = (2)𝑥
2.
𝑦 = 3𝑒 𝑥
y
7
6
5
4
3
2
1
y
(2,4)
(1,2)
(0,1)
-4
-3
-2
-1
18
16
14
12
10
8
6 (1,8.15)
4
2
1
-1
x
2
3
4
-3
(0,3)
-2 (-1,1.1)
-1 -2
1
x
2
3
3. The number of cell phone subscribers 𝑦 (in millions) can be approximated by the model
𝑦 = 233(1.06)𝑡 , where 𝑡 is the number of years since 2006.
a. Tell whether the model represents exponential growth or exponential decay.
Growth; b-value is bigger than 1
b. Identify the annual percent increase or decrease in the population.
6% increase
c. Estimate when the number of subscribers will be 300,000,000.
About 4 years
4.
You deposit $6000 in an account that pays 4.25% annual interest. Find the balance after
𝑟 𝑛𝑡
4 years when the interest is compounded semi-annually. 𝐴 = 𝑃 (1 + 𝑛)
. 0425 2(4)
)
𝐴 = 6000 (1 +
= $7,099.17
2
Simplify the expression.
5.
8𝑒 7
24𝑒 9
1
3𝑒 2
Algebra II Chapter 6 Test—LT #27-#33
6.
(3𝑒 2𝑥 )4
34 𝑒 8𝑥 = 81𝑒 8𝑥
Practice Test
Learning Target #29: I can evaluate and simplify logarithm expressions.
7.
Rewrite log 6 36 = 2 in exponential form. 8.
62 = 36
1
Rewrite 8−2 = 64 in logarithmic form.
log 8
Evaluate the logarithm.
9.
log 9 81
10.
9? = 81
2
log 2
1
= −2
64
1
8
2? =
−3
Find the inverse of the function.
11. 𝑦 = 7𝑥
12.
1
8
𝑦 = log(4𝑥)
10𝑥
4
log 7 𝑥
Learning Target #30: I can graph logarithmic functions.
Learning Target #31: I can perform transformations of exponential and logarithmic functions.
Describe the transformation of 𝒇(𝒙) represented by 𝒈(𝒙). Then graph 𝒈(𝒙).
𝑓 (𝑥 ) = 4𝑥 ; 𝑔(𝑥 ) = 4𝑥−1 + 1
13.
14.
1 𝑥
1 𝑥+2
𝑓 (𝑥 ) = ( ) ; 𝑔 ( 𝑥 ) = ( )
−1
2
2
Right 1 and Up 1
Left 2 and Down 1
y
(1,2)
(0,1.25)
Algebra II Chapter 6 Test—LT #27-#33
y
x
(-4,3)
(-3,1)
(-2,0)
x
Practice Test
Write a rule for 𝐠.
Let the graph of g be a horizontal stretch by a factor of 2, followed by a translation 4
15.
units right and 3 units down of the graph of 𝑓(𝑥 ) = 4𝑥 .
1
𝑔(𝑥 ) = 4(2)𝑥−4 − 3
16.
Let the graph of g be a translation 3 units right, followed by a reflection in the 𝑥-axis
of the graph of 𝑓 (𝑥 ) = 9𝑥 .
𝑔(𝑥 ) = −9𝑥−3
Graph the function.
𝑓 (𝑥 ) = log 4 (𝑥 + 1) − 2
17.
9 y
8
7
6
5
4
3
2
1
Left 1 and Down 2
x
-1 -1 1 2 3 4 5 6 7 8 9
-2
(3,-1)
-3
(0,-2)
-4
Use the Change of Base Formula to evaluate each expression. Show your work and
round your answer to four decimal places.
1
log 4 64
18.
19.
log 4
1024
log 64
=3
1
log 4
log (1024)
= −5
log 4
Learning Target #32: I can apply properties of logarithms.
Expand or condense the logarithmic expression.
log 5 7𝑐
20.
21.
log 3 81 + 5 log 3 2
log 5 7 + log 5 𝐶
22.
log 4 + 2 log 3 − log 9
log
4 ∗ 32
9
Algebra II Chapter 6 Test—LT #27-#33
log 3 81 ∗ 25
23.
𝑥 3
log ( )
𝑤
3 log 𝑥 − 3 log 𝑤
Practice Test
Learning Target #33: I can solve exponential and logarithmic equations and inequalities.
Solve the equation/inequality. Round to the nearest hundredth when necessary.
24.
25.
2𝑒 5𝑥 = 26
53𝑥−2 = 1252𝑥+5
log 53𝑥−2 = log 1252𝑥+5
(3𝑥 − 2) log 5 = (2𝑥 + 5) log 125
3𝑥 − 2 = (2𝑥 + 5)(3)
3𝑥 − 2 = 6𝑥 + 15
−17 = 3𝑥
17
𝑥=−
3
𝑒 5𝑥 = 13
ln 𝑒 5𝑥 = ln 13
5𝑥 = ln 13
𝑥 ≈ .51
26.
34𝑥−5 < 8
27.
log 34𝑥−5 < log 8
(4𝑥 − 5) log 3 < log 8
4𝑥 − 5 < 1.89279
𝑥 < 1.72
28.
log 2 3𝑥 = log 2 (4𝑥 − 2)
log 7 2(𝑥 + 5) = 10
710 = 2𝑥 + 10
𝑥 = 141,237,619.5
29.
4 log 2 𝑥 − log 2 5 = log 2 125
2
log 6 𝑥 = 3
2
63 = 𝑥
𝑥 ≈ 3.30
3𝑥 = 4𝑥 − 2
𝑥=2
30.
log 7 2 + log 7 (𝑥 + 5) = 10
31.
ln 𝑥 + ln(𝑥 − 1) = 6
𝑥4
log 2
= log 2 125
5
4
𝑥
= 125
5
𝑥 4 = 625
𝑥=5
Algebra II Chapter 6 Test—LT #27-#33
Practice Test