Question

Consider a population that begins growing exponentially at a base rate of 5% per year and then follows a logistic growth pattern. I the carrying capacity is 80 million, find the logistic growth rate when the population is 20 milion.

Answer 1

The logistic growth rate when the population is 20 million with a carrying capacity of 80 million and an intrinsic growth rate of 5% is 0.75 million individuals per year.

Step-by-step explanation:

When a population begins to grow exponentially and then transitions to logistic growth, the logistic growth rate can be found using the formula for logistic growth Population growth = rN(K - N) / K, where r represents the intrinsic growth rate, N represents the current population size, K represents the carrying capacity, and (K - N) represents the remaining population growth potential.

In this scenario, the population is growing at an exponential base rate of 5% per year with a carrying capacity of 80 million. When the population size is 20 million, we want to find the logistic growth rate. We are given that the intrinsic growth rate r is 5% or 0.05 per year. Therefore, we use the logistic growth formula to get Population growth = 0.05 * 20 million * (80 million - 20 million) / 80 million. Simplifying this gives us Population growth = 0.05 * 20 million * 60 million / 80 million which is Population growth = 0.05 * 15 million, equating to a logistic growth rate of 0.75 million individuals per year at the population size of 20 million.