Question

A population of deer in Florida grows according to a logistic model, with r = 0.17 and K = 10,000. At what population size is the per capita population growth rate the highest? Group of answer choices N = 1000 N = 5000 N = 8000 N = 10000

Answer 1

The per capita population growth rate is highest when the population size is half of the carrying capacity (K) in a logistic model.

Step-by-step explanation:

The per capita population growth rate is the highest when the population size is equal to half of the carrying capacity (K) in a logistic model. In this case, K is given as 10,000, so the population size at which the per capita population growth rate is the highest would be N = 5000.

Answer 2

N = 1000

Step-by-step explanation:

The population growth of species per capita of any geographical can be computed by using the formula:

`(dN)/(dT)=rN (1 - (N)/(K))`

here;

N = population chance

T = time taken

K = carrying capacity

r = the constant exponential growth rate

From the given equation, we can posit that the value of r will be the greatest at the time the value of dN is highest:

As such, when the population chance = 1000

`(dN)/(dT)=0.17 * 1000 (1 - (1000)/(10000))`

`(dN)/(dT)=0.17 * 1000 (0.9)`

`(dN)/(dT)= 153`

At N = 5000;

`(dN)/(dT)= 85`

At N= 8000;

`(dN)/(dT)= 34`

At N = 10000

`(dN)/(dT)= 0`