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.