Question

A population of 50 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 500 deer. Absent constraints, the population would grow by 40% per year.

Estimate the population after one year

p1 =


Estimate the population after two years

p2=

Answer 1

p1 = 70 deer

p2 = 98 deer

Explanation:

We use the population growth expression:

`N(t)=N_0\,(1+r)^t`

which in our case renders:

`N(t)=N_0\,(1+r)^t\\N(t)=50\,(1+0.4) ^t\\N(t)=50\,(1.4) ^t`

Therefore, after 1 year the population would be:

`N(1)=50\,(1.4) ^1=70`

giving a total of 70 deer

and after two years, it would be:

`N(2)=50\,(1.4) ^2=98`