Question

A population of deer inside a park has a carrying capacity of 200 and a growth rate of 3%. If the initial population is 80 deer, what is the population of deer at any given time?

Answer 1

The population of deer at any given time = 200(e^0.03t) ÷ (1.5 + (e^0.03t))

Explanation:

This is an example of logistic equation on population growth

carrying capacity, k = 200

Rate, r = 3% = 0.03

Initial Population, P1 = 80

P(t) =?

P(t) = (P1 (k)(e^rt)) ÷ (k- P1 + P1(e^rt))

P(t) = (80 (200)(e^0.03t)) ÷ (200 - 80 + 80(e^0.03t))

= (16000(e^0.03t)) ÷ (120 + 80(e^0.03t))

= 200(e^0.03t) ÷ (1.5 + (e^0.03t))