Question 1

The cumulative number F of flu cases reported after t weeks is modeled by the function  . The maximum number of people who can be expected to get the flu is (round your answer to two decimal places, if necessary)
​
A) 1,398.00
B) 2,796
C) 71.69
D) 38

Accepted Answer

B

Question 2

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function  . ​
According to the model, how many Americans had Internet access in 1990? Round your answer to two decimal places, if necessary.
​
A) 194 million
B) 97.00 million
C) 100 million
D) 1.92 million

Accepted Answer

D

Question 3

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function  . According to this model, what is the maximum number of Americans who will ever have Internet access? Round your answer to two decimal places , if necessary.
​
A) 198.8 million
B) 99.40 million
C) 2.16 million
D) 91 million

Accepted Answer

A

Question 4

Magazine circulation after t years is modeled by the function  . The largest magazine circulation that can be expected is (round your answer to two decimal places, if necessary)
​
A) 11.00 thousand
B) 22 thousand
C) 5.50 thousand
D) 3 thousand

Accepted Answer

The answer of Magazine circulation after t years is modeled...

Question 5

A logistic function always has a limiting value.

Accepted Answer

A logistic function models growth that increases exponentially at first and then slows down as it approaches a maximum limit, known as the carrying capacity or the limiting value.

Question 6

For a logistic function, the function shows a maximum growth rate at half the limiting value.

Accepted Answer

The logistic function models growth that starts exponentially, but slows down as it approaches a maximum limit (carrying capacity). The maximum growth rate occurs at half the carrying capacity, where the growth rate changes most rapidly.

Question 7

A logistic population model shows the most rapid population growth at the inflection point.

Accepted Answer

The inflection point in a logistic population model represents the point of maximum growth rate, where the population is growing most rapidly due to an optimal balance of resources and population size.

Question 8

The cumulative number F of flu cases reported after t weeks is modeled by the function  . How many people had the flu at the start of the epidemic? Round your answer to the nearest whole number.
​
A) 
B) 
C) 
D)

Accepted Answer

The answer of The cumulative number F of flu cases...

Question 9

For a logistic function, the point of inflection and the limiting value are the same.

Accepted Answer

The point of inflection of a logistic function is where the second derivative changes sign, typically at the midpoint of the function's growth, whereas the limiting value (also known as the carrying capacity) is the maximum value that the function approaches as its input goes to infinity.

Question 10

Enrollment at a certain university t years after 2000 is given by  . What is the enrollment in 2000? Round your answer to two decimal places, if necessary.
​
A) 
B) 
C) 
D)

Accepted Answer

The answer of Enrollment at a certain university t years...

Question 11

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function  . ​
For what value of N is Internet access growing at the fastest rate? Round your answer to two decimal places, if necessary.
​
A) 
B) 
C) 
D)

Accepted Answer

The answer of The number N, in millions, of Americans...

Question 12

The cumulative number F of flu cases reported after t weeks is modeled by the function  . For what cumulative number of flu cases is the disease spreading at the fastest rate? Round your answer to two decimal places, if necessary.
​
A) 
B) 
C) 
D)

Accepted Answer

The answer of The cumulative number F of flu cases...

Question 13

The cumulative number F of flu cases reported after t weeks is modeled by the function  . For what value of t will the cumulative number of flu cases be 1,101.00? Round your answer to two decimal places.
​
A) 
B) 
C) 
D)

Accepted Answer

The answer of The cumulative number F of flu cases...

Question 14

Logistic regression is appropriate for all data sets that are neither exponential nor linear.

Accepted Answer

Logistic regression is specifically designed for binary classification problems, not for fitting or modeling all types of data distributions. It models the probability that a given input belongs to a particular category.

Question 15

Enrollment at a certain university t years after 2000 is given by  . At what enrollment level is enrollment growing at the fastest rate? Round your answer to two decimal places, if necessary.
​
A) 
B) 
C) 
D)

Accepted Answer

The answer of Enrollment at a certain university t years...

Question 16

A population is modeled by the function  . What is the initial value of the population? Round your answer to two decimal places, if necessary.
​
A) 
B) 
C) 
D)

Accepted Answer

The answer of A population is modeled by the function...

Question 17

A population is modeled by the function  . ​
The limiting value of the population is (round to two decimal places, if necessary)
​
A) 2,835
B) 1,417.50
C) 405.00
D) 6

Accepted Answer

The answer of A population is modeled by the function...

Question 18

The theory of maximum sustainable yield says that a renewable resource that grows logistically should be harvested at the carrying capacity.

Accepted Answer

The theory of maximum sustainable yield suggests that the maximum rate at which a renewable resource can be harvested without impairing its ability to regenerate is at half the carrying capacity, not at the carrying capacity itself.

Question 19

Enrollment at a certain university t years after 2000 is given by  . According to the model, what is the maximum enrollment that can be attained? Round your answer to two decimal places, if necessary.
​
A) 10,853.00
B) 21,706
C) 5,426.50
D) 22,031

Accepted Answer

The answer of Enrollment at a certain university t years...

Question 20

A population is modeled by the function  . For what value of N is the population growing at the fastest rate? Round your answer to two decimal places, if necessary.
​
A) 
B) 
C) 
D)

Accepted Answer

The answer of A population is modeled by the function...

Quiz 21: Logistic Functions

The cumulative number F of flu cases reported after t weeks is modeled by the function . The maximum number of people who can be expected to get the flu is (round your answer to two decimal places, if necessary)

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function . According to the model, how many Americans had Internet access in 1990? Round your answer to two decimal places, if necessary.

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function . According to this model, what is the maximum number of Americans who will ever have Internet access? Round your answer to two decimal places , if necessary.

Magazine circulation after t years is modeled by the function . The largest magazine circulation that can be expected is (round your answer to two decimal places, if necessary)

A logistic function always has a limiting value.

For a logistic function, the function shows a maximum growth rate at half the limiting value.

A logistic population model shows the most rapid population growth at the inflection point.

The cumulative number F of flu cases reported after t weeks is modeled by the function . How many people had the flu at the start of the epidemic? Round your answer to the nearest whole number.

For a logistic function, the point of inflection and the limiting value are the same.

Enrollment at a certain university t years after 2000 is given by . What is the enrollment in 2000? Round your answer to two decimal places, if necessary.

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function . For what value of N is Internet access growing at the fastest rate? Round your answer to two decimal places, if necessary.

The cumulative number F of flu cases reported after t weeks is modeled by the function . For what cumulative number of flu cases is the disease spreading at the fastest rate? Round your answer to two decimal places, if necessary.

The cumulative number F of flu cases reported after t weeks is modeled by the function . For what value of t will the cumulative number of flu cases be 1,101.00? Round your answer to two decimal places.

Logistic regression is appropriate for all data sets that are neither exponential nor linear.

Enrollment at a certain university t years after 2000 is given by . At what enrollment level is enrollment growing at the fastest rate? Round your answer to two decimal places, if necessary.

A population is modeled by the function . What is the initial value of the population? Round your answer to two decimal places, if necessary.

A population is modeled by the function . The limiting value of the population is (round to two decimal places, if necessary)

The theory of maximum sustainable yield says that a renewable resource that grows logistically should be harvested at the carrying capacity.

Enrollment at a certain university t years after 2000 is given by . According to the model, what is the maximum enrollment that can be attained? Round your answer to two decimal places, if necessary.

A population is modeled by the function . For what value of N is the population growing at the fastest rate? Round your answer to two decimal places, if necessary.

Quiz 21: Logistic Functions

The cumulative number F of flu cases reported after t weeks is modeled by the function . The maximum number of people who can be expected to get the flu is (round your answer to two decimal places, if necessary) ​

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function . ​ According to the model, how many Americans had Internet access in 1990? Round your answer to two decimal places, if necessary. ​

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function . According to this model, what is the maximum number of Americans who will ever have Internet access? Round your answer to two decimal places , if necessary. ​

Magazine circulation after t years is modeled by the function . The largest magazine circulation that can be expected is (round your answer to two decimal places, if necessary) ​

A logistic function always has a limiting value.

For a logistic function, the function shows a maximum growth rate at half the limiting value.

A logistic population model shows the most rapid population growth at the inflection point.

The cumulative number F of flu cases reported after t weeks is modeled by the function . How many people had the flu at the start of the epidemic? Round your answer to the nearest whole number. ​

For a logistic function, the point of inflection and the limiting value are the same.

Enrollment at a certain university t years after 2000 is given by . What is the enrollment in 2000? Round your answer to two decimal places, if necessary. ​

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function . ​ For what value of N is Internet access growing at the fastest rate? Round your answer to two decimal places, if necessary. ​

The cumulative number F of flu cases reported after t weeks is modeled by the function . For what cumulative number of flu cases is the disease spreading at the fastest rate? Round your answer to two decimal places, if necessary. ​

The cumulative number F of flu cases reported after t weeks is modeled by the function . For what value of t will the cumulative number of flu cases be 1,101.00? Round your answer to two decimal places. ​

Logistic regression is appropriate for all data sets that are neither exponential nor linear.

Enrollment at a certain university t years after 2000 is given by . At what enrollment level is enrollment growing at the fastest rate? Round your answer to two decimal places, if necessary. ​

A population is modeled by the function . What is the initial value of the population? Round your answer to two decimal places, if necessary. ​

A population is modeled by the function . ​ The limiting value of the population is (round to two decimal places, if necessary) ​

The theory of maximum sustainable yield says that a renewable resource that grows logistically should be harvested at the carrying capacity.

Enrollment at a certain university t years after 2000 is given by . According to the model, what is the maximum enrollment that can be attained? Round your answer to two decimal places, if necessary. ​

A population is modeled by the function . For what value of N is the population growing at the fastest rate? Round your answer to two decimal places, if necessary. ​

The cumulative number F of flu cases reported after t weeks is modeled by the function . The maximum number of people who can be expected to get the flu is (round your answer to two decimal places, if necessary)

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function . According to the model, how many Americans had Internet access in 1990? Round your answer to two decimal places, if necessary.

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function . According to this model, what is the maximum number of Americans who will ever have Internet access? Round your answer to two decimal places , if necessary.

Magazine circulation after t years is modeled by the function . The largest magazine circulation that can be expected is (round your answer to two decimal places, if necessary)

The cumulative number F of flu cases reported after t weeks is modeled by the function . How many people had the flu at the start of the epidemic? Round your answer to the nearest whole number.

Enrollment at a certain university t years after 2000 is given by . What is the enrollment in 2000? Round your answer to two decimal places, if necessary.

The number N, in millions, of Americans with Internet access t years after 1990 is modeled by the function . For what value of N is Internet access growing at the fastest rate? Round your answer to two decimal places, if necessary.

The cumulative number F of flu cases reported after t weeks is modeled by the function . For what cumulative number of flu cases is the disease spreading at the fastest rate? Round your answer to two decimal places, if necessary.

The cumulative number F of flu cases reported after t weeks is modeled by the function . For what value of t will the cumulative number of flu cases be 1,101.00? Round your answer to two decimal places.

Enrollment at a certain university t years after 2000 is given by . At what enrollment level is enrollment growing at the fastest rate? Round your answer to two decimal places, if necessary.

A population is modeled by the function . What is the initial value of the population? Round your answer to two decimal places, if necessary.

A population is modeled by the function . The limiting value of the population is (round to two decimal places, if necessary)

Enrollment at a certain university t years after 2000 is given by . According to the model, what is the maximum enrollment that can be attained? Round your answer to two decimal places, if necessary.

A population is modeled by the function . For what value of N is the population growing at the fastest rate? Round your answer to two decimal places, if necessary.