Answer:
a) [tex]P(t) = 22000(1.071)^{t}[/tex]
b) The population increases 7.1% each year.
Step-by-step explanation:
The continuous population growth model is given by:
[tex]P(t) = P_{0}(1+r)^{t}[/tex]
In which [tex]P(t)[/tex] is the population after t years, [tex]P_{0}[/tex] 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 [tex]P_{0} = 22000, r = 0.071[/tex]
a) Write a function to model the population increase.
[tex]P(t) = 22000(1 + 0.071)~{t}[/tex]
[tex]P(t) = 22000(1.071)^{t}[/tex]
b) By what percent does the populaiion increase each year?
[tex]r = 0.071[/tex]
So the population increases 7.1% each year.
