Exam 6: Section 4: Differential Equations

The logistic function models the growth of a population. Determine when the population reaches of the maximum carrying capacity. Round your answer to three decimal places.

Find the logistic equation that satisfies the following differential equation and initial condition.

Each of the following graphs is from a logistic function . Which one has the smallest value of b?

Match the logistic equation and initial condition with the graph of the solution.

A conservation organization releases 30 panthers into a preserve. After 3 years, there are 50 panthers in the preserve. The preserve has a carrying capacity of 150. Determine the time it takes for the population to reach 110.

The logistic function models the growth of a population. Identify the initial population.

The logistic function models the growth of a population. Determine when the population reaches one-half of the maximum carrying capacity. Round your answer to three decimal places.

The logistic function models the growth of a population. Identify the maximum carrying capacity.

Identify the graph of the logistic function .

A conservation organization releases 40 coyotes into a preserve. After 4 years, there are 70 coyotes in the preserve. The preserve has a carrying capacity of 175. Write a logistic function that models the population of coyotes in the preserve.

Match the logistic differential equation and initial condition with the graph of its solution shown below.

The logistic function models the growth of a population. Identify the value of k.

Each of the following graphs is from a logistic function . Which one has the largest value of b?

A conservation organization releases 50 foxes into a preserve. After 5 years, there are 85 foxes in the preserve. The preserve has a carrying capacity of 225. Determine the population after 10 years. Discard any fractional part of your answer.