Question

A population of squirrels on an island has a carrying capacity of 350 individuals. If the maximum rate of increase is 1.0 per individual per year and the population size is 275, determine the population growth rate (Round to the nearest whole number).

Answer 1

Answer:

The population growth rate is 59 squirrels per year.

Step-by-step explanation:

Given:

A population of squirrels on an island has a carrying capacity of 350 individuals. If the maximum rate of increase is 1.0 per individual per year and the population size is 275.

Now, to find the population growth rate.

Carrying capacity ($K$) = 350.

Maximum rate ($r_{max}$) = 1.0 per individual per year.

Population size ($N$) = 275.

Now, to get the population growth rate we put formula:

$\frac{dN}{dT}= r_{max}\frac{K-N}{K}N$

$\frac{dN}{dT}=1.0\times \frac{350-275}{350}\times 275\\\\\frac{dN}{dT}=1.0\times \frac{75}{350}\times 275\\\\\frac{dN}{dT}=1.0\times 0.214\times 275\\\\\frac{dN}{dT}=58.85.$

So, rounding to nearest whole number of the population growth rate is 59 squirrels per year.

Therefore, the population growth rate is 59 squirrels per year.