Module 15: Interpreting Concavity for Logistic Functions Quiz

Step 1 of 1

The logistic function in the following graph models the number of rabbits on an island since rabbits were introduced to the island in 1900.

[The graph of a logistic function is shown, representing the number of rabbits on an island on the y-axis compared to the years since 1900 on the x-axis. From Point A to Point B, the number of rabbits on the island is concave up.]2018 WGU, Powered by GeoGebra

Question 1 of 5

Question1

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Which statement is correct?

From A to B, the function is concave up, implying the rabbit population was increasing more and more slowly from 1900 to 1908.

From A to B, the function is concave down, implying the rabbit population was increasing more and more slowly from 1900 to 1908.

From A to B, the function is concave down, implying the rabbit population was increasing faster and faster from 1900 to 1908.

From A to B, the function is concave up, implying the rabbit population was increasing faster and faster from 1900 to 1908.

Johan manages web and email servers for Progress Hospital. Each email user is required to electronically sign an agreement. This function models the percentage of employees who have signed the agreement since the first email reminder was sent and is depicted in the following graph.

[The graph of a logistic function is shown, representing the percentage of employees who have signed an agreement on the y-axis compared to the days since a reminder was sent on the x-axis. From Point A to Point B, the percentage of employees who have signed the agreement is increasing at a decreasing rate.]2018 WGU, Powered by GeoGebra

Question 2 of 5

Question2

This is not a form; we suggest that you use the browse mode and read all parts of the question carefully.

Which statement is true?

You cannot tell the concavity without the function's equation.

From Point A to Point B, the function is concave down.

From Point A to Point B, the functiondoes nothave concavity.

From Point A to Point B, the function is concave up.

A rumor was spreading among students since school started at 9:00a.m. The following graph depicts the function to model the percentage of students who learned the rumor on that day.

[The graph has Hours Since 9 a.m. plotted on the x axis and Percent of Students plotted on the y axis. A curve begins at (0, 2), rises to about (3, 60), and then rises more steeply before turning almost horizontal through (5.5, 98).]2018 WGU, Powered by GeoGebra

Question 3 of 5

Question3

This is not a form; we suggest that you use the browse mode and read all parts of the question carefully.

Which statement is true?

From 1:00 p.m.to 2:00 p.m., the rumor was spreading faster and faster.

From 11:00 a.m.to 2:00 p.m., the rumor was spreading slower and slower.

From 1:00 p.m.to 2:00 p.m., the rumor was spreading slower and slower.

From 1:00 p.m.to 2:00 p.m., the percentage of students knowing the rumor was decreasing.

Sunrise Sky Spa started opening tanning salons in a small city in early 2000. Sunrise experienced exponential growth and became a major brand in its market. This logistic function can be used to model Sunrise Sky Spa's tanning salon market share, in percentage, in its city

S(t)=401+150e0.7tS(t)=401+150e0.7t,

wheretis the number of years since 2000. This function is depicted in the following graph.

[The graph has Years Since 2000 plotted on the x axis and Market Share in Percentage plotted on the y axis. A curve begins at (0, 0), rises to about (14, 40), and then turns almost horizontal through (18, 40).]2018 WGU, Powered by GeoGebra

Question 4 of 5

Question4

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If Sunrise Sky Spa's CEO is focusing primarily on total market share, would the CEO prefer the segment of the graph from 2000 to 2007 or from 2007 on, and why?

The CEO would prefer the segment from 2000 to 2007, because the company's market share was increasing at a faster and faster pace.

The CEO would prefer the segment from 2007 on, because the company had more market share.

The CEO would prefer the segment from 2000 to 2007, because the company's market share was increasing at a slower and slower pace.

The CEO would prefer the segment from 2007 on, because the company's market share was increasing at a faster and faster pace.

A rumor was spreading among students since school started at 9:00a.m. The following graph depicts the function to model the percentage of students who learned the rumor on that day.

[The graph has Hours Since 9 a.m. plotted on the x axis and Percent of Students plotted on the y axis. A curve begins at (0, 2), rises to about (3, 60), and then rises more steeply before turning almost horizontal through (5.5, 98).]2018 WGU, Powered by GeoGebra

Question 5 of 5

Question5

This is not a form; we suggest that you use the browse mode and read all parts of the question carefully.

Which statement is true?

From 10:00a.m.to 11:00 a.m., the rumor was spreading faster and faster.

From 10:00a.m.to 11:00a.m., the rumor was spreading slower and slower.

From 11:00a.m.to 1:00p.m., the rumor was spreading faster and faster.

From 11:00a.m.to 1:00p.m., the rumor was spreading slower and slower.