Question

Apopulation grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.a) Write a function to model the population increase.b) By what percent does the populaiion increase each year?

Answer 1

Answer:

a) $P(t) = 22000(1.071)^{t}$

b) The population increases 7.1% each year.

Step-by-step explanation:

The continuous population growth model is given by:

$P(t) = P_{0}(1+r)^{t}$

In which $P(t)$ is the population after t years, $P_{0}$ is the initial population and r is the growth rate.

In this problem, we have that:

A population grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.

This means that $P_{0} = 22000, r = 0.071$

a) Write a function to model the population increase.

$P(t) = 22000(1 + 0.071)~{t}$

$P(t) = 22000(1.071)^{t}$

b) By what percent does the populaiion increase each year?

$r = 0.071$

So the population increases 7.1% each year.