Module 16: Interpreting Asymptotes for Logistic Function Quiz

Step 1 of 1

Movie Mania offers discounted movie tickets. The logistic function,M(t)M(t), in the following graph is used to model the number of memberships since 2000, in millions, wheretis the number of years since 2000.

[A graph shows a curve that begins just below y equals 60, falls in the first quadrant through (30, 20) and turns horizontal passing through (50, 10).]2018 WGU, Powered by GeoGebra

Question 1 of 5

Question1

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What does the upper asymptote indicate?

There were about 6 members in the years prior to 2000.

There were about 6 million members in the years to 2000.

The number of memberships stabilized at about 2 million.

There were about 6 thousand members in the years prior to 2000.

A new state law took effect in January 2010 with a tax break for tax filers who contribute to college tuition accounts for their children. The percentageof tax payers who participated in this program since January 2010 can be modeled by the logisticfunctionP(t)P(t), wheretis the number of months since January 2010.P(t)P(t)is depicted in the followinggraph.

[The graph has Months plotted on the x axis and Percentage of Tax Payers plotted on the y axis. A curve labeled P of t begins at (0, 10), rises in the first quadrant through (6, 40), and then rises almost horizontally through (20, 55).]2018 WGU, Powered by GeoGebra

Question 2 of 5

Question2

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What does the upper asymptote tell us?

Prior to January 2010, the percentage of tax payers was stable at 55%.

Prior to January 20210, the percentage of tax payers was stable at 10%

In the long run, the percentage of tax payers stabilizes at 10%.

In the long run, the percentage of tax payers stabilizes at 55%.

Question 3 of 5

Question3

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Traditional bookstores like Good Read have been struggling due to the growthofonline retailers.Annual revenues of Good Read, in millions of dollars, can be modeledby a logistic function,P(t)P(t), which decreased from a maximum of $8.5 million to $1.5 million.

Which of these couldbeP(t)P(t)'s equation?

P(t)=71+0.01e0.4t+1.5P(t)=71+0.01e0.4t+1.5

P(t)=8.51+0.01e0.4t+1.5P(t)=8.51+0.01e0.4t+1.5

P(t)=8.51+0.01e0.4t+1.5P(t)=8.51+0.01e0.4t+1.5

P(t)=71+0.01e0.4t+1.5P(t)=71+0.01e0.4t+1.5

Question 4 of 5

Question4

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A new state law took effect in January 2010 with a tax break for tax filers who contribute to college tuition accounts for their children. The percentageof tax payers who participated in this program since January 2010 can be modeled by the logisticfunctionP(t)P(t), wheretis the number of months since January 2010.

If the percentage of tax payers increased from 20% to 50% since the new law took effect, which of these couldbeP(t)P(t)'s equation?

P(t)=501+10e0.4t+20P(t)=501+10e0.4t+20

P(t)=201+10e0.4t+30P(t)=201+10e0.4t+30

P(t)=301+10e0.4t+20P(t)=301+10e0.4t+20

P(t)=501+10e0.4tP(t)=501+10e0.4t

Question 5 of 5

Question5

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Movie Mania offers discounted movie tickets. A logistic function,

M(t)=2.51+0.03e0.6t+1.5M(t)=2.51+0.03e0.6t+1.5,

isused to model the number of memberships since 2000, in millions, wheretis the number of years since 2000.

Which statement is correct?

The maximum number of members is2.5 million, and eventually the number decreased to 1.5 million.

The maximum number of members is 4 million, and that number eventually decreased to 1.5 million.

The maximum number of members is 4 million, and that number eventually decreased to 1 million.

The maximum number of members is 3 million, and that number eventually decreased to 1.5 million.

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