The logistic model can be used for situations in which the initial population P₀ is above the carrying capacity K. For example, consider a deer population of 1500 on an island where a large fire has reduced the carrying capacity to 1000 deer.
a. Assuming a base growth rate of r₀ = 0.1 and an initial population of P(0) = 1500, write a logistic growth function for the deer population and graph it. Based on the graph, what happens to the deer population in the long run?
b. How fast (in deer per year) is the population declining immediately after the fire at t = 0?
c. How long does it take for the deer population to decline to 1200 deer?