Worksheet: The Logistic Model

In practising through this worksheet, we will learn about the logistic population growth model, where the population cannot exceed an amount fixed by the environment called the carrying capacity.

Q1:

Suppose a population’s growth is governed by the logistic equation where . Write a formula for .

Q2:

Suppose a population grows according to a logistic model with a carrying capacity of 4 000 and . If the initial population is 800, find the population after 20 years.

Q3:

A population after time weeks is modeled by the logistic equation . If , what population does the model predict when ?

Q4:

A population after time weeks is modeled by the logistic equation . If , what population does the model predict after 9 weeks?

Q5:

Suppose a population grows according to a logistic model with a carrying capacity of 2 500 and . Write the logistic differential equation for this information.