Question

A population of 350 animals has a growth rate of 5% each year. Write an exponential function to model this situation.

Answer 1

Given:

The population of animals = 350

Growth rate = 5% each year.

To find:

The exponential function to model this situation.

Solution:

The general exponential growth model is:

`f(t)=a(1+r)^t`

Where, a is the initial value, r is the growth rate in decimal and t is the time period.

Substituting
`a=350, r=0.05` in the above formula, we get

`f(t)=350(1+0.05)^t`

`f(t)=350(1.05)^t`

Therefore, the required exponential function is
`f(t)=350(1.05)^t`, where f(t) is the number of animals after t years.