A population of aphids is growing logistically.If the carrying capacity is 2,000 and the per capita growth rate is 0.1 per day, at what size will the population be increasing by 50 aphids per day?
A) 1,000
B) 1,500
C) 2,000
D) 3,000
E) 20,000

Question

Quizplus · Accepted Answer

The logistic growth model is given by the equation dN/dt = rN(1 - N/K), where dN/dt is the rate of population growth, r is the per capita growth rate, N is the population size, and K is the carrying capacity. To find the population size (N) where the growth rate is 50 aphids per day, we set dN/dt = 50, r = 0.1, and K = 2000. Substituting these values into the equation gives 50 = 0.1N(1 - N/2000). Solving for N, we find that N = 1000.

A Population of Aphids Is Growing Logistically