The Growth Rate of Three-Toed Sloth Population in a Tropical Forest

Population Growth Equations

A population of three-toed sloths in a tropical forest has a maximum per capita growth rate of 0.8 per year. The population size is limited by the carrying capacity of the forest, which is 500 individuals.

Question:

Which of the following is the growth rate of the sloth population when the population is made up of 275 individuals?

Choose 1 answer:

A 99 sloths per year.

B 220 sloths per year.

C 374 sloths per year.

D 400 sloths per year.

Final Answer:

The growth rate of the sloth population when it is made up of 275 individuals is 0.36 individuals per year.

Explanation:

The growth rate of the sloth population when it is made up of 275 individuals can be calculated using the logistic growth equation:

Growth rate = r * (1 - (Population size/Carrying capacity))

Given that the maximum per capita growth rate (r) is 0.8 and the carrying capacity is 500, we can substitute these values into the equation:

Growth rate = 0.8 * (1 - (275/500))

Growth rate = 0.8 * (1 - 0.55)

Growth rate = 0.8 * 0.45

Growth rate = 0.36

Therefore, the growth rate of the sloth population when it is made up of 275 individuals is 0.36 individuals per year.