Question

Assume there is a certain population of deer in a forest whose growth is described by the logistic equation. The constant of proportionality for this type of deer is k=0.59, and the carrying capacity of the forest is 10,000 deer.

If the starting population is 8800 deer, then after one breeding season the population of the forest is?

Answer 1

I solved it! I got 9297.2222 so no need to help

Answer 2

We can use the logistic equation to model the growth of the deer population:

dP/dt = k * P * (1 - P/K)

where P is the population of deer, t is time, k is the constant of proportionality, and K is the carrying capacity of the forest.

Using the given values, we have:

dP/dt = 0.59 * 8800 * (1 - 8800/10000)
dP/dt = 0.59 * 8800 * 0.12
dP/dt = 628.32

This means that the population of the forest will increase by 628.32 deer after one breeding season. Therefore, the new population will be:

8800 + 628.32 = 9428 (rounded to the nearest whole number)

So, the population of the forest after one breeding season will be about 9428 deer.