Calculating Growth Rate of Sloth Population
What is the growth rate of the sloth population when the population is made up of 275 individuals?
A. 99 sloths per year
B. 220 sloths per year
C. 374 sloths per year
D. 400 sloths per year
Answer:
99 sloths per year are the growth rate of the sloth population when it is made up of 275 individuals and is close to its carrying capacity. Here option A is the correct answer.
The growth rate of the sloth population can be estimated using the logistic growth model. This model describes the population growth of a species that is limited by its carrying capacity (K) and has a maximum per capita growth rate (r). The growth rate of the population is given by:
dN/dt = r × N × (1 - N/K)
where N is the current population size, and dN/dt is the change in population size over time.
Plugging in the values, we get:
dN/dt = 0.8 × 275 × (1 - 275/500)
= 0.8 × 275 × (1 - 0.55)
= 0.8 × 275 × 0.45
= 99 sloths per year.