# Section 5- 1 Logistic Functions

Business

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Q 4Q 4

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

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Q 7Q 7

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

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Q 8Q 8

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

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Multiple Choice

Q 9Q 9

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

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Multiple Choice

Q 10Q 10

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

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Multiple Choice

Q 11Q 11

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

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Q 12Q 12

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)

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Q 13Q 13

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)

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Q 14Q 14

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)

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Q 15Q 15

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)

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Q 16Q 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)

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Q 17Q 17

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)

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Q 18Q 18

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

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Q 19Q 19

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)

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Q 20Q 20

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)

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Q 21Q 21

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)

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Q 22Q 22

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

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Q 23Q 23

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)

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Q 24Q 24

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)

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Q 25Q 25

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

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Q 26Q 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

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Multiple Choice

Q 27Q 27

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)

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Q 28Q 28

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)

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Q 29Q 29

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)

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Q 30Q 30

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)

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Q 32Q 32

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

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Multiple Choice

Q 33Q 33

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

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Q 34Q 34

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

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Q 35Q 35

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

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Multiple Choice