Expert answer:Unit 9 Lesson 5 math
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Complete the sentence with the best answer.
An exponential model should be used to model data if:
A scatter plot of ln y versus ln x fits a linear pattern.
A scatter plot of y versus ln x fits a linear pattern.
A scatter plot of y versus x fits a linear pattern.
A scatter plot of ln y versus x fits a linear pattern.
Which system of equations can be used to find the exponential function that passes through the
points (2, 254)) and (4, 6254)?
2=a(254)b4=a(6254)b
254=ab26254=ab4
254=a(2)b6254=a(4)b
2=ab2544=ab6254
Which system of equations can be used to find the power function that passes through the points (2,
10) and (8, 25)?
Complete the sentence with the best answer.
A power model should be used to model data if:
A scatter plot of ln y versus ln x fits a linear pattern.
A scatter plot of ln y versus x fits a linear pattern.
A scatter plot of y versus ln x fits a linear pattern.
A scatter plot of y versus x fits a linear pattern.
Which table of values shows ln y versus x for the data below?
Which of the following exponential models can be used to model the data below?
Which exponential function goes through the points
and
?
Which of the following tables of values shows ln y versus ln x for the data points below?
Which of the following power models can be used to model the data below?
Find a power function that passes through the points (2.9, 9.4) and (7.3, 12.8).
Which of the following equations shows the logarithmic equation below in exponential form?
Which of the following equations shows the logarithmic equation below in exponential form?
Which of the following logarithms is equal to 1?
Evaluate the logarithm
-2
2
1/2
-1/2
without a calvulator.
Use a calculator to evaluate log 6. Round to three decimal places.
1.732
0.778
1.792
2.449
Simplfy the expression
Log x
log 2
x
Find the inverse of the function y = log7 49x
y=2x
y=7x
What is the domain and range of the graph of the function below?
y = log (x-2)
Domain: all real numbers; Range: y > 2
Domain: all real numbers; Range: y < 2
Domain: x > 2; Range: all real numbers
Domain: x < 2; Range: all real numbers
The Richter scale is used for measuring the magnitude of an earthquake. The Richter magnitude R is
given by the model below, where E is the energy (in kilowatt-hours) released by the earthquake.
R = 0.67 log (0.37E) + 1.46
Suppose an earthquake releases 14,500,000,000 kilowatt-hours of energy. What is the earthquake’s
magnitude? Round to three decimal places.
4.400
3.979
8.268
7.979
Students and teachers at a school were polled to see if they were in favor of extending the parking
lot into part of the athletic fields. The results of the poll are shown in the two-way table below.
Which of the following statements is false?
In Favor Not in Favor
Students
16
23
Teachers
9
14
Thirty-nine students were polled in all.
Fourteen teachers were polled in all.
Twenty-three students are not in favor of extending the parking lot.
Nine teachers are in favor of extending the parking lot.
The table below shows the results of a poll in which randomly selected high school students were
asked if they prefer Football or Basketball. What is the marginal relative frequency of 12th graders?
9th Grade 10th Grade 11th Grade 12th Grade
Football
12
8
12
7
Basketball
5
10
7
9
0.4375
0.5625
0.2286
0.1
The table below shows the results of a poll in which randomly selected high school students were
asked if they prefer Football or Basketball. What is the joint relative frequency of 10th graders who
like football?
9th Grade 10th Grade 11th Grade 12th Grade
Football
12
8
12
7
Basketball
5
10
7
9
0.1143
0.1429
0.4444
0.3077
The table below shows the results of a poll in which randomly selected high school students were
asked if they prefer virtual or traditional schools. What is the marginal relative frequency of students
who prefer traditional school?
9th Grade 10th Grade 11th Grade 12th Grade
Virtual
9
14
17
20
Traditional
17
16
5
2
0.06
0.6
0.04
0.4
The table below shows the results of a poll in which randomly selected high school students were
asked if they prefer virtual or traditional schools. If you are given a student who prefers virtual
school, what is the probability that the student is also a 12th grader?
9th Grade 10th Grade 11th Grade 12th Grade
Virtual
9
14
17
20
Traditional
17
16
5
2
about 0.33
about 0.91
about 0.25
about 0.20
Students and teachers at a school were polled to see if they were in favor of extending the parking
lot into part of the athletic fields. The results of the poll are shown in the two-way table below. What
is the probability that someone who is a student is also in favor of extending the parking lot into part
of the athletic fields?
In Favor Not in Favor
Students
16
23
Teachers
9
14
about 0.64
about 0.26
about 0.41
about 0.16
The table below shows the results of a poll in which randomly selected high school students were
asked if they prefer virtual or traditional schools. What is the joint relative frequency of 9th graders
who prefer virtual schools?
9th Grade 10th Grade 11th Grade 12th Grade
Virtual
9
14
17
20
Traditional
17
16
5
2
0.09
0.17
0.3462
0.15
Chuck is the owner of a car dealership. He is assessing the success rates of his top three salespeople
in order to offer one of them a promotion. Over two months, for each attempted sale, he records
whether the salesperson made a successful sale or not. The results are shown in the table below.
Which salesperson has the highest success rate?
Successful Unsuccessful
Rachel
6
4
Jeff
5
5
Bill
8
7
Jennifer
3
6
Rachel
Jeff
Bill
Jennifer
Four competing basketball teams in ABC county are competing to go to the state basketball
championship. The team with the highest win rate will go to the championship. Which team would
be selected to go?
Win
Loss
Barracudas
13
3
Sharks
10
3
Sixers
12
1
Hawks
8
2
Barracudas
Sharks
Sixers
Hawks
What is the domain of the exponential function below?
All negative numbers.
All positive numbers.
All real numbers except 0.
All real numbers.
What is the range of the exponential function below?
All positive numbers.
All real numbers except 0.
All real numbers.
All negative numbers.
Describe the transformation of the graph
translated 4 units left and 1 unit up.
translated 4 units right and 1 unit up.
translated 4 units left and 1 unit down.
translated 4 units right and 1 unit down.
from the parent graph,
The amount g (in trillions of cubic feet) of natural gas consumed in the United States from 1940 to
1970 can be modeled by the equation below, where t is the number of years since 1940.
g = 2.91(1.07)t
Estimate the natural gas consumption in 1945.
4.12 trillion cubic feet.
4.08 trillion cubic feet
61.12 trillion cubic feet
15.57 trillion cubic feet
Which exponential growth model would model the following situation:
You buy a commemorative coin for $105. Each year t, the value V of the coin increases by 3%
V = 105(0.03)t
V = 0.03(105)t
V = 105(1.03)t
V = 105(3)t
The student enrollment E of a high school was 1200 in 1990 and increased by 12% per year until
1998. Which exponential growth model shows the school’s student enrollment in terms of t, the
number of years since 1990?
E = 12(1200)t
E = 1200(1.12)t
E = 1200(12)t
E = 1.15(1240)t
You deposit $1500 in a bank account. Find the balance after 2 years if the account has an interest
rate of 2.5% and is compounded monthly.
$1575.94
$1576.82
$1506.27
$9375
You want to have $3000 in your bank account after 5 years. How much should you deposit into a
bank account that pays 3.25% interest compounded quarterly? Round to the nearest dollar.
$2551
$2881
$3527
$2552
…
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