Question 1
A population of rabbits follows a logistic growth pattern. The population starts with 18
rabbits and the equilibrium population is 90. After 8 years there are 54 rabbits.
1. Determine the population function 𝑁(𝑡).
2. How long will it take for the population to reach 85 rabbits?
Question 2
A fish population in a dam follows logistic growth. Initially there are 25 fish, and the
carrying capacity is 200 fish. After 6 months the population has grown to 80 fish.
1. Find the logistic growth equation.
2. Determine when the population reaches 180 fish.
Question 3
A colony of bacteria begins with 40 bacteria. The maximum sustainable population is
500 bacteria. After 3 hours, there are 140 bacteria.
1. Determine the logistic growth model.
2. Find the time when the population reaches 450 bacteria.
Question 4
A deer population starts at 30 deer. The equilibrium population is 150 deer. After 10
years, the population has increased to 75 deer.
1. Find the logistic growth function.
2. Determine how many years it takes for the population to reach 145 deer.
Question 5
A population of foxes follows logistic growth. Initially there are 12 foxes, and the
carrying capacity is 100 foxes. After 9 years, there are 48 foxes.
1. Determine the logistic equation.
2. How long until the population reaches 95 foxes?
Question 6
A wildlife reserve contains 60 antelope initially. The carrying capacity is 300 antelope.
After 5 years, there are 120 antelope.
1. Determine the population function.
2. Find the time required for the population to reach 290 antelope.
Question 7
A town's population follows logistic growth. Initially there are 2 000 people, and the
maximum population is 10 000 people. After 12 years, there are 5 000 people.
1. Determine the logistic growth equation.
2. Estimate when the population reaches 9 500 people.
Question 8
A population of insects begins with 100 insects. The carrying capacity is 600 insects.
After 4 weeks, there are 250 insects.
1. Determine the logistic model.
2. Find when the population reaches 550 insects.
A population of rabbits follows a logistic growth pattern. The population starts with 18
rabbits and the equilibrium population is 90. After 8 years there are 54 rabbits.
1. Determine the population function 𝑁(𝑡).
2. How long will it take for the population to reach 85 rabbits?
Question 2
A fish population in a dam follows logistic growth. Initially there are 25 fish, and the
carrying capacity is 200 fish. After 6 months the population has grown to 80 fish.
1. Find the logistic growth equation.
2. Determine when the population reaches 180 fish.
Question 3
A colony of bacteria begins with 40 bacteria. The maximum sustainable population is
500 bacteria. After 3 hours, there are 140 bacteria.
1. Determine the logistic growth model.
2. Find the time when the population reaches 450 bacteria.
Question 4
A deer population starts at 30 deer. The equilibrium population is 150 deer. After 10
years, the population has increased to 75 deer.
1. Find the logistic growth function.
2. Determine how many years it takes for the population to reach 145 deer.
Question 5
A population of foxes follows logistic growth. Initially there are 12 foxes, and the
carrying capacity is 100 foxes. After 9 years, there are 48 foxes.
1. Determine the logistic equation.
2. How long until the population reaches 95 foxes?
Question 6
A wildlife reserve contains 60 antelope initially. The carrying capacity is 300 antelope.
After 5 years, there are 120 antelope.
1. Determine the population function.
2. Find the time required for the population to reach 290 antelope.
Question 7
A town's population follows logistic growth. Initially there are 2 000 people, and the
maximum population is 10 000 people. After 12 years, there are 5 000 people.
1. Determine the logistic growth equation.
2. Estimate when the population reaches 9 500 people.
Question 8
A population of insects begins with 100 insects. The carrying capacity is 600 insects.
After 4 weeks, there are 250 insects.
1. Determine the logistic model.
2. Find when the population reaches 550 insects.
