Question

A population of 30 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain up to 400 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

Answer: The population after one year P(1) = 42.

The population after two years P(2) = 59.

Step-by-step explanation:

We know that the exponential growth equation is given by :-

$y= A(1+r)^x$

, where A = initial value.

r= rate of growth

x= time period.

As per given , we have

A = 30

r= 0.40

Then, the population function for deer will become : $P(x)=30(1.40)^x$

At x= 1 , we have

$P(1)=30(1.40)^1=42$

At x=2  , we have

$P(1)=30(1.40)^2=58.8\approx59$

Hence, the population after one year P(1) is 42.

The population after two years P(2) = 59.