Download 1 Graph y log(x 1)

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Class: _____________ Date: __________
Exponentials/Logs Multiple Choice Post-Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1 Graph y = log(x + 1) − 7
A
B
C
D
____
2 The pH of a liquid is a measure of how acidic or basic it is. The concentration of hydrogen ions in a
ÈÍ ˘˙
liquid is labeled ÍÍÍ H + ˙˙˙ . Use the formula pH = −log [H + ] to answer questions about pH.
Î ˚
Find the pH level, to the nearest tenth, of a liquid with [H+] about 6.5x 10 −3 .
A 3.8
B 2.2
____
____
C -3.8
D 3.0
3 Write the logarithmic expression as a single logarithm: 5 log b q + 2 log b y
A log b (q 5 y 2 )
C log b (q 5 + y 2 )
B
D log b ÊÁÁ qy 5 + 2 ˆ˜˜
(5 + 2) log b (q + y)
4 Expand the logarithmic expression: log 7
A −x log7 2
B
log 7 x
log 7 2
Ë
¯
x
2
C log 7 2 − log 7 x
D log 7 x − log 7 2
____
5 Use the properties of logarithms to evaluate log 3 9 + log 3 36 − log 3 4.
A 2
C 8
B 4
D 41
____
6 Use a graphing calculator. Solve 5 4x = 2115 by graphing. Round to the nearest hundredth.
A 1.19
B 0.83
Algebra II Exponentials Post-Test
C 8
D 41
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____
7 Use the Change of Base Formula to solve 2 2x = 90. Round to the nearest ten-thousandth.
A 7.6133
B 9.3658
____
C 3.2459
D 12.9837
8 Which value of x satisfies the equation 2(5 x ) = 250?
A 1
B 2
____
C 3
D 4
9 The half-life of Carbon-14 is about 5730 years. It was determined that a bone specimen contained about
35% of Carbon-14. Which type of function models the number of years ago that this animal was alive?
A Linear
B Quadratic
____
10 Identify the logarithmic form of 10 0.602 = 4
A log 10 0.602 =
B
____
C Exponential
D Logarithmic
log 10
1
4
1
= 0.602
4
C log 10 4 = −0.602
D log 10 4 = 0.602
11 Which of the following represents a shift of 5 units left and 6 units down from the graph of
f(x) = log x?
A g(x) = log(x + 5) − 6
B g(x) = log(x + 5) + 6
____
C g(x) = log(x − 5) − 6
D g(x) = log(x − 5) + 6
12 Solve log(4x + 10) = 3.
7
4
247.5
A −
C 250
B
D 990
Algebra II Exponentials Post-Test
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____
____
13 What is the inverse of the function y = log 2 (x + 5)?
A
y = 2x
C
y = 2x + 5
B
y = log −2 (x − 5)
D
y = 2x − 5
14 The amount of money in an account with continuously compounded interest is given by the formula
A = Pe rt , where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the
nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded
continuously at 6.2%. Round to the nearest tenth.
A 1.1 yr
B 6.9 yr
____
15 Solve 15 2x = 36. Round to the nearest ten-thousandth.
A 0.6616
B 2.6466
____
C 11.2 yr
D 0.6 yr
C 1.7509
D 1.9091
16 Determine what family of functions models the graph below, then write a function for the graph.
A exponential, y = 0.5(2) x
B exponential, y = 2(0.5) x
Algebra II Exponentials Post-Test
C exponential, y = (2 ⋅ 0.5) x
D logarithmic, y = 2(5) x
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____
ÊÁ 1 ˆ˜ x
17 Determine which of the following is a graph of y = 7 ÁÁÁÁ ˜˜˜˜ , then state the asymptote.
Ë 4¯
A
C
asymptote: x = 0
B
D
asymptote: x = –4
____
asymptote: x = 7
asymptote: x = 0
18 Find the annual percent increase or decrease that y = 0.35(2.3) x models.
A 230% increase
B 130% increase
Algebra II Exponentials Post-Test
C 30% decrease
D 65% decrease
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____
19 For an annual rate of change of –31%, find the corresponding growth or decay factor.
A 0.31
B 0.69
____
C 1.31
D 1.69
20 How much money invested at 5% compounded continuously for 3 years will yield $820?
A $952.70
B $818.84
____
C $780.01
D $705.78
21 Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will
you have in the account after 4 years?
A $800.26
B $6,701.28
____
C $10,138.07
D $1,923.23
22 The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of
801 kg. Write an exponential function that models the decay of this material. Find how much radioactive
material remains after 10 days. Round your answer to the nearest thousandth.
1
____
A
x
1 ÊÁ 1 ˜˜˜ˆ 85
y = ÁÁÁÁ
; 0.228 kg
2 Ë 801 ˜˜¯
B
ÊÁ 1 ˜ˆ 85 x
y = 801 ÁÁÁÁ ˜˜˜˜ ; 0 kg
Ë 2¯
1
C
ÊÁ 1 ˜ˆ 85 x
y = 801ÁÁÁÁ ˜˜˜˜
; 738.273kg
Ë 2¯
D
ÊÁ 1 ˜ˆ 85 x
˜˜
y = 2 ÁÁÁÁ
; 0.911 kg
˜
Ë 801 ˜¯
1
23 What is the inverse of the function: f(x) = 4 x − 4?
A
B
f −1 (x) = 4 −x + 4
−1
1
x
f (x) = 4 + 4
Algebra II Exponentials Post-Test
C
f −1 (x) = log 4 (x + 4)
D
f −1 (x) = log(x + 4)
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____
24 Graph y = 7 (6)
A
x+2
B
____
+ 1.
C
D
25 Evaluate log 0.01
A –10
B –2
Algebra II Exponentials Post-Test
C 2
D 10
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____
26 Write the equation log 32 8 =
3
in exponential form.
5
3
A 32 5 = 8
C
ÊÁ 3 ˜ˆ 32
ÁÁ ˜˜ = 8
ÁÁ 5 ˜˜
Ë ¯
3
B
____
____
8
5
5
= 32
27 Evaluate log 3 81
A 4
B -4
D 8 3 = 32
C 3
D 2
28 Decibels (dB) are defined by the equation; 10log
I
, where I o = 10−12 , the intensity of a barely audible
Io
sound. Use the formula to determine the loudness in dB of a busy street, which measures an intensity of
10−5 .
A 10 dB
B 70 dB
____
29 Write an exponential function y = ab x for a graph that includes (1, 15) and (0, 6).
A
B
____
C -17 dB
D 7 dB
y = 6(2.5) x
y = 2(5) x
C
D
y = 2.5(6) x
y = 6(2) x
30 An initial population of 725 quail increases at an annual rate of 5%. Write an exponential function to
model the quail population.
A
B
f(x) = 725(.05) x
f(x) = 725(1.05) x
Algebra II Exponentials Post-Test
C
D
f(x) = 725(5) x
f(x) = (725 ⋅ 0.05)
x
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____
1
2
31 Rewrite in logarithmic form ( ) x = y
1
2
A x = logy
C log 1 y = x
2
B
log x = y
1
2
D log 1 x = y
2
____
2
3
32 Solve the equation (x − 7) = 4
A 11
B 1; -1
____
C -3
D 15; -1
33 If there are initially 1500 bacteria in a culture, and the number of bacteria double each hour, the
number of bacteria after t hours can be found using the formula N = 1500(2 t ). How long will it take
the culture to grow to 50,000 bacteria?
A 5.06 hr
B 24.25 hr
Algebra II Exponentials Post-Test
C 3.04 hr
D 1.52 hr
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