If K (carrying capacity) for a population is 1,200, and r = 0.1, which of the following populations will show the greatest increase over the course of one year assuming exponential growth?
A)N = 100
B)N = 200
C)N = 300
D)N = 700
E)N = 900

Question

Quizplus · Accepted Answer

The formula for exponential growth is Nt = Noe^rt, where Nt is the population after time t, No is the initial population, e is the base of the natural logarithm, r is the growth rate, and t is time. Given K = 1,200 and r = 0.1, we can calculate the theoretical maximum growth rate as K/2 = 600. Therefore, any population smaller than 600 will show an increase greater than 600 individuals over one year. Of the answer choices given, only population E (N = 900) is greater than 600, and therefore it will show the greatest increase over the course of one year assuming exponential growth.

If K (Carrying Capacity) for a Population Is 1,200, and R