Question

Consider a population that begins growing exponentially at a base rate of 5% per year and then follows a logistic growth pattern. If 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 is 0.0375.

Step-by-step explanation:

The logistic growth rate for a population can be determined using the formula: r = r_max * (K - N) / K, where r is the logistic growth rate, r_max is the intrinsic growth rate, K is the carrying capacity, and N is the population size. In this case, the population is growing exponentially at a base rate of 5% per year. To find the logistic growth rate when the population is 20 million, we need to first find the intrinsic growth rate, which is 5%.

Given:

• Base exponential growth rate: 5%
• Carrying capacity: 80 million
• Population size: 20 million

Using the formula, we can calculate the logistic growth rate:

r = 0.05 * (80 - 20) / 80 = 0.05 * 60 / 80 = 0.0375

Therefore, when the population is 20 million, the logistic growth rate is 0.0375.