Deck 21: Logistic Functions

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

Answer 1

2,796

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

Answer 2

1.92 million

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

Answer 3

198.8 million

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

Question 5

A logistic function always has a limiting value.

Question 6

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

Question 7

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

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)

Question 9

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

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)

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)

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)

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)

Question 14

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

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)

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)

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

Question 18

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

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

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)

Question 21

Magazine circulation after t years is modeled by the function . ​
At what circulation level is magazine circulation growing at the fastest rate? Round your answer to two decimal places, if necessary.
​

A) 11.00 thousand
B) 22 thousand
C) 3.67 thousand
D) 5 thousand

Question 22

A population is modeled by the function . For what value of t will the population reach 3,626.00? Round your answer to two decimal places.
​

A)
B)
C)
D)

Question 23

Magazine circulation after t years is modeled by the function . ​
When was the circulation increasing at the fastest rate? Round your answer to two decimal places.
​

A) After 4.90 years
B) After 3.35 years
C) After 3.67 years
D) After 3.54 years

Question 24

Make a logistic model for enrollment at a university t years after 2000 making use of the following information. A University facilities can accommodate at most 5,829 students.
B: Enrollment in 2000 is 2,116.
C: In the absence of limiting factors, enrollment would grow by 13% per year.
​
​

A)
B)
C)
D)

Question 25

Make a logistic model for the cumulative number of disease cases in a cattle herd reported after t weeks. A There are a total of 308 animals susceptible to the disease.
B: There are initially 6 diseased animals.
C: In the absence of limiting factors, the cumulative number of diseased animals would grow by 27% per week.
​​

A)
B)
C)
D)

Question 26

The number N, in millions, of Americans with Internet access t years after calendar year 1990 is modeled by the function . According to the model, for which calendar year is Internet access growing at the fastest rate? Round your answer to the nearest whole number.
​

A) 2000
B) 2001
C) 1997
D) 2003

Question 27

Make a logistic model , with t in years, for a population that satisfies all of the following conditions: A The carrying capacity is .
B: The initial value is .
C: In the absence of limiting factors, N would grow by 19% per year.
​​

A)
B)
C)
D)

Question 28

Magazine circulation after t years is modeled by the function . ​
When did magazine circulation reach 10.00 thousand? Round your answer to two decimal places.
​

A) After 6.17 years
B) After 5.80 years
C) After 4.20 years
D) After 3.00 years

Question 29

Show the graph of a logistic function.​ ​

A) ​
B) ​
C) ​
D) ​

Question 30

Enrollment at a certain university t years after calendar year 2000 is given by . According to the model, for which calendar year will enrollment reach 24,363.00? Round your answer to the nearest whole number.
​

A) 2010
B) 2007
C) 2005
D) 2012

Question 31

A population is modeled by the function . What value of t corresponds to the point of inflection? Round your answer to two decimal places.
​

A)
B)
C)
D)

Question 32

The number N, in millions, of Americans with Internet access t years after calendar year 1990 is modeled by the function . ​
For what calendar year will the number of Americans with Internet access reach 133.70 million? Round your answer to the nearest whole number.
​

A)
B)
C)
D)

Question 33

Enrollment at a certain university t years after calendar year 2000 is given by . According to the model, for which calendar year is enrollment growing at the fastest rate? Round your answer to the nearest whole number.
​

A) 2006
B) 2009
C) 2010
D) 2004

Question 34

The cumulative number F of flu cases reported after t weeks is modeled by the function . For what value of t is the epidemic spreading most rapidly? Round your answer to two decimal places.
​

A)
B)
C)
D)

Question 35

Magazine circulation after t years is modeled by the function . ​
What was the initial magazine circulation? Round your answer to two decimal places, if necessary.
​

A) 11.50 thousand
B) 23 thousand
C) 5.75 thousand
D) 3 thousand