If a population of 5,000 zebras is growing logistically and has a carrying capacity of 10,000, what would the per capita rate of increase be if the population grew by 50 zebras in one year?

Question

Quizplus · Accepted Answer

The logistic growth equation is:
dN/dt = rN(1-N/K)

where:
dN/dt is the rate of change in population size over time
r is the intrinsic rate of increase
N is the population size
K is the carrying capacity

To find the per capita rate of increase (r), we can use the formula:

r = (dN/dt) / N

We know that the population grew by 50 zebras, so dN/dt = 50. The initial population size is 5,000 and the carrying capacity is 10,000. We can use these values to find K/N:

K/N = 10,000 / 5,000 = 2

Now we can plug in all the values:

r = (50/5,000) / (1 + 2(5,000/10,000)) = 0.02

Therefore, the per capita rate of increase is 0.02 or 2%. The best choice is C) 0.02.

If a Population of 5,000 Zebras Is Growing Logistically and Has