Module 12: Interpreting Asymptotes for Exponential Functions Quiz

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Question 1 of 14

Question1

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Polynomials never have asymptotes. Why not?

A polynomial's graph equals a specificy-value in both the positive and the negative directions.

A polynomial's graph equals a specificy-value in either the positive or the negative direction, but not both.

A polynomial's graph never approaches a specificy-value in either the positive or the negative direction.

The number of bed bugsxdays after an infestation begins is modeled by the function shown in the following graph.

[A graph shows a curve that rises with increasing steepness through about (0, 6), (5, 7), and (10, 13.5).]

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Question 2 of 14

Question2

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What is the horizontal asymptote, and what does it mean?

The equation of the horizontal asymptote isy= 6, which means that there were 6 bed bugs when the infestation started.

The equation of the horizontal asymptote isy= 0, which means that the infestation started at time 0.

The equation of the horizontal asymptote isy= 0, which means that there were 0 bed bugs when the infestation started.

The equation of the horizontal asymptote isy= 6, which means that the maximum number of bed bugs is 6.

A pot of water is brought to a boil and then removed from the stove. The temperature of the water, in degrees Celsius,xminutes after being removed from heat is modeled by the function shown in the following graph.

[A graph shows a curve that falls with decreasing steepness through about (0, 100), (10, 45), (30, 25), and (60, 20).]2018 WGU, Powered by GeoGebra

Question 3 of 14

Question3

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What is the horizontal asymptote, and what does it mean?

The equation of the horizontal asymptote isy= 0, which means that the water's temperature approaches 0 degrees Celsius as time goes on.

The equation of the horizontal asymptote isy= 100, which means that the maximum temperature of the water is 100 degrees Celsius.

The equation of the horizontal asymptote isy= 20, which means that the temperature of the water tendstoward20 degrees Celsius as it sits.

The equation of the horizontal asymptote isy= 80, which means that the temperature of the water has reached its minimum by minute 80.

A customer service line is very busy andit isimportant for representatives to answer questions quickly and move on to the next call. Withxrepresentatives answering calls, the time to answer a question (in minutes on they-axis) can be modeled by the function in the followinggraph.

[A graph shows a concave-up curve that falls with decreasing steepness through about (0, 12), (5, 6), and (30, 3).]2018 WGU, Powered by GeoGebra

Question 4 of 14

Question4

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What is the horizontal asymptote, and what does it mean?

The equation of the horizontal asymptote isy= 0, which means that as the number of representatives answering questions increases, the time it takes to answer a question approaches 0 minutes.

The equation of the horizontal asymptote isy= 12.5, which is the time needed to answer 0 questions.

The equation of the horizontal asymptote isy= 3, which means that as the number of representatives answering questions increases, the time that it takes to answer a question approaches 3 minutes.

The equation of the horizontal asymptote isy= 10, which means that the optimal number of representatives is 10, since it takes 4 minutes to answer a question.

A company releases version 3.3 of an app. The number of users, in millions, of the 3.2 version of the appxweeks after version 3.3 is released is modeled by the function shown in the following graph.

[A graph shows a curve that falls with decreasing steepness through about (0, 25), (5, 12), (15, 9), and (45, 5).] 2018 WGU, Powered by GeoGebra

Question 5 of 14

Question5

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What is the horizontal asymptote, and what does it mean?

The equation of the horizontal asymptote isy= 5, which means that the number of users increases to and stays at 5 million as time passes.

The equation of the horizontal asymptote isy= 5, which means that about 5 million usersdo notupgrade to version 3.3.

The equation of the horizontal asymptote isy= 25, which means that the number of users decreases to and stays at 25 million.

The equation of the horizontalasymptoteisy= 25, which means that the number of users increases to and stays at 25 million.

The function models the number of fish in a fish tankxmonths after it was purchased, as seen in the following graph.

[A graph shows a concave up curve that rises with increasing steepness in the second quadrant and passes through (15, 70) and (30, 104).]2018 WGU, Powered by GeoGebra

Question 6 of 14

Question6

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Does the function have a horizontal asymptote?

Yes, because the function gets really close to thex-axis but never crosses it.

Yes, because asxgets closer to 0, they-value of the function appears to get closer to 66.

No, because asxgets big, they-value of the function continues to increase.

No, because the function does not get closer to thex-axis.

The value of a house in thousands of dollarsxyears after purchase is modeled by the function in thisgraph.

[The graph of an exponential function is shown with years since purchase on the x-axis and home value in thousands on the y-axis.Use the following sample coordinates to determine the asymptote in this graph: (0, 158.80),(10, 189.64),(20, 197.39),(30, 199.34),(40, 199.84). ] 2018 WGU, Powered by GeoGebra

Question 7 of 14

Question7

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Estimate the equation of the horizontal asymptote.

y= 160

y= 200

y= 40

There is no horizontal asymptote.

The number of people in an office,xhours after noon on a Friday, is modeled by the function in the followinggraph.

[A graph shows a curve that rises with increasing steepness through about (0, 6), (5, 7), and (10, 13.5).]

2018 WGU, Powered by GeoGebra

Question 8 of 14

Question8

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What does the horizontal asymptote mean?

The office is empty by 5:30.

There were more people in the office at 4:00 than at 6:00.

There were about 500 people in the office for most of the morning.

There are more people leaving at 2:00 than 4:00.

Question 9 of 14

Question9

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A person'sbody metabolizes half of the caffeine in the bloodstream in approximately 6 hours. If a person drinks a cup of coffee containing 40 milligrams of caffeine, the amount of caffeine in her bloodstream afterxhours is modeled by a function.

In a graph, what would be the horizontal asymptote of the function, and what does it mean?

The equation of the horizontal asymptote isy= 0, which means that the amount of caffeine will get closer to 0 milligrams as time passes.

The equation of the horizontal asymptote isy= 20, which means that the amount of caffeine in the bloodstream will be 20 milligrams.

The equation of the horizontal asymptote isy= 6, which means that the half-life of caffeine is 6 hours.

The equation of the horizontal asymptote isy= 40, which means that there will never be more than 40 milligrams of caffeine in the bloodstream.

A company releases version 3.3 of an app. The number of users, in millions, of this new version of the appxweeks after the version is released is modeled by the function shown in the following graph.

[A graph shows a curve that rises with increasing steepness through approximately (10, 5), (20, 7), (30, 12), and (40, 25). ] 2018 WGU, Powered by GeoGebra

Question 10 of 14

Question10

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What is the horizontal asymptote, and what does it mean?

The equation of the horizontal asymptote isy= 40, which means that about 40 million people upgraded on the launch day and other users slowly started using the new version.

The equation of the horizontal asymptote isy= 4, which means that about 4 million people upgraded on the launch day and, slowly at first, other users started using the new version.

The equation of the horizontal asymptote isy= 0, which means that the lowest number of users is 0.

The equation of the horizontal asymptote isy= 25, which means that about 25 million people upgraded on the launch day and other users slowly started using the new version.

Thenumberof bacteria in a sample, expressed in millions,xdays after an antibiotic is administered, is modeled by the function shown in the following graph.

[The curve falls almost horizontally from the second quadrant to the first quadrant through approximately (0, 5), then turns, and falls with increasing steepness through approximately (10.5, 4) and (19.5, 0).] 2018 WGU, Powered by GeoGebra

Question 11 of 14

Question11

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What is the equation for the horizontal asymptote and what does it mean?

The equation of the horizontal asymptote isy= 19, which means that all the bacteria have died by hour 19.

The equation of the horizontal asymptote isy= 5, which means that the sample stayed at around 5 million bacteria while the antibiotics began to work.

The equation of the horizontal asymptote isy= 11, which means that the number of bacteria starts to decrease faster after 11 hours.

The equation of the horizontal asymptote isy= 0, which means that the number of bacteria will be 0 after 19 hours.

Question 12 of 14

Question12

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Which function's graph shows that it has a horizontal asymptote?

[The curve rises steeply through about (negative 1, 0), changes direction at about (1, 5), falls to about (3, negative 2), then rises steeply through quadrant 1.]2018 WGU, Powered by GeoGebra

[A graph shows a line that passes through (0, 30), (10, 50), and (20, 70).]

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[A graph shows a concave up curve that falls with decreasing steepness in the first quadrant through (10, 38) and then turns almost horizontal approaching the x axis at about x equals 50.]

2018 WGU, Powered by GeoGebra

[A graph shows a concave down curve that begins at (0, 0) and rises with decreasing steepness through (25, 5).]2018 WGU, Powered by GeoGebra

A video is posted on an online site and people begin to view it. The number of people, in thousands, who have watched the videoxhours after it was posted can be modeled by the function shown in the following graph.

[A graph shows a concave-up curve that rises almost horizontally through (0, 100) and (20, 100), then turns almost vertical and rises through approximately (60, 148).]2018 WGU, Powered by GeoGebra

Question 13 of 14

Question13

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What is the horizontal asymptote, and what does it mean?

The equation of the horizontal asymptote isy= 100, which means that there were 100,000 people watching the video every hour.

The equation of the horizontal asymptote isy= 100, which means that there were 100 people watching the video every hour.

The equation of the horizontal asymptote isy= 100, which means that there were consistently about 100,000 people watching the video for quite some time after it was initially released.

The equation of the horizontal asymptote isy= 100, which means that there were consistently about 100 people watching the video for quite some time after it was initially released.

The number of deer in a county, in thousands,xyears after a major highway is built is modeled by the function in the followinggraph.

[A graph shows a concave up curve that passes through (0, 8), falls in the first quadrant, and then turns almost horizontal through (8, 2) and (10, 2).]2018 WGU, Powered by GeoGebra

Question 14 of 14

Question14

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Estimate the equation of the horizontal asymptote.

y= 10

y= 0

y= 2

y= 8

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