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?
If the starting population is 8800 deer, then after one breeding season the population of the forest is?
Answers
Bot
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.
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.
I solved it! I got 9297.2222 so no need to help