The logistic function models the growth of a population.Identify the value of k.

Question

The logistic function  models the growth of a population.Identify the value of k. ​

Quizplus · Accepted Answer

The logistic function is typically written as P(t) = L/(1+ae^-kt), where L is the carrying capacity, a is the initial population, t is time, and k is the growth rate parameter. Since the problem statement does not provide values for L or a, we cannot solve for k directly. However, we can use the fact that the logistic function is sigmoidal (S-shaped) to narrow down our choices for k. Specifically, we know that the inflection point (i.e. the point where the slope of the curve is steepest) occurs at t=0.5L/k, and that the slope of the curve at this point is k/4. Looking at the answer choices, we see that only choice C results in a value of k/4 that is within a reasonable range (i.e. k/4 = 2/4 = 0.5). Therefore, we can reasonably conclude that choice C is correct.

The Logistic Function Models the Growth of a Population