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

Answer:

N = 1000

Step-by-step explanation:

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

$\dfrac{dN}{dT}=rN (1 - \dfrac{N}{K})$

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

$\dfrac{dN}{dT}=0.17 * 1000 (1 - \dfrac{1000}{10000})$

$\dfrac{dN}{dT}=0.17 * 1000 (0.9)$

$\dfrac{dN}{dT}= 153$

At N = 5000;

$\dfrac{dN}{dT}= 85$

At N= 8000;

$\dfrac{dN}{dT}= 34$

At N = 10000

$\dfrac{dN}{dT}= 0$