Question

A population of snails has an annual per capita birth rate of 0.055 and an annual per capita death rate of 0.015.

Calculate an estimate of the change in population size over one year, for a given starting population of 1,000 individuals. Assume that the population grows exponentially according to the equation dN/dt = r^N.

A) increases by 40 individuals
B) decreases by 15 individuals
C) increases by 400 individuals
D) increases by 55 individuals
E) decreases by 20 individuals

Answer 1

Option A, increases by 40 individuals

Step-by-step explanation:

Given,

Annual per capita birth rate
`= 0.055`

Annual per capita death rate
`= 0.015`

Net per capita population growth rate

`= 0.055 - 0.015\\= 0.040`

The growth equation of population

`(dN)/(dt) = r^N` Eq 1

On simplifying we get

`N = N_0 * e^(-rt)\\`

Substituting the given values in Eq 1, we get -

`(dN)/(dt) = 0.04 * 1000\\(dN)/(dt) = 40`

Hence, the population increase by
`40` individuals.

Option A is correct