Module 16: Interpreting Asymptotes for Logistic Function Quiz

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Question 1 of 5

Question1

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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 modeled by this function:

R(t)=7.51+0.01e0.4t+2.5R(t)=7.51+0.01e0.4t+2.5,

wheretis the number of years since 2000.

Which statement is correct?

The function increases from a minimum of 2.5 to a maximum of 10.

The function decreases from a maximum of 10 to a minimum of 2.5.

The function decreases from a maximum of 10 to a minimum of 5.

The function decreases from a maximum of 7.5 to a minimum of 2.5.

Traditional bookstores like Good Read have been struggling due to the growthofonline retailers. Annual revenues of Good Read, in millions of dollars, can be modeled by the function in the graph.

[The graph has Years Since 2000 plotted on the x axis and Revenue in Millions of Dollars plotted on the y axis. A curve labeled R of t begins at (0, 7), then falls in the first quadrant and passes through (6, 5), and then turns almost horizontal.]2018 WGU, Powered by GeoGebra

Question 2 of 5

Question2

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What does the upper asymptote indicate?

In the long run, the revenue stabilized at 2 million dollars.

Prior to 2000, revenue was stable at about 7 million dollars.

Prior to 2000, the revenue was stable at about 7 thousand dollars.

In the long run, the revenue stabilized at 2 thousand dollars.

Question 3 of 5

Question3

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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 4 of 5

Question4

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Movie Mania offers discounted movie tickets. Its memberships stabilized at 3 million for a few years until 2000. In 2000, the company reported financial troubles,and many members cancelled their memberships. By 2010, memberships stabilized at 1 million.

A logistic function,M(t)=L1+Cekt+mM(t)=L1+Cekt+m,is used to model the number of memberships since 2000, in millions, wheretis the number of years since 2000.

Which of these could be the correct equationofM(t)M(t)?

M(t)=21+0.03e0.6t+1M(t)=21+0.03e0.6t+1

M(t)=31+0.03e0.6tM(t)=31+0.03e0.6t

M(t)=11+0.03e0.6t+2M(t)=11+0.03e0.6t+2

M(t)=21+0.03e0.6t+1M(t)=21+0.03e0.6t+1

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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