Exam 21: Logistic Functions

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. ​

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 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 . For what value of t will the cumulative number of flu cases be 1,101.00? Round your answer to two decimal places. ​

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. ​

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. ​​

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

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 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. ​

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

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. ​ ​

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

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 . For what value of N is the population growing at the fastest rate? 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 . For what value of t is the epidemic spreading most rapidly? Round your answer to two decimal places. ​

A logistic function always has a limiting value.

Show the graph of a logistic function.​ ​

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. ​​