Question

Find the exponential function that satisfies the given conditions. Initial value = 30, increasing at a rate of 13% per year

Answer 1

30(1+0.13)^x ask me if you need an explanation

Answer 2

The exponential function that satisfies the given conditions is
`P(t)=30(1.13)^t`.

Explanation:

If a population
`P` is changing at a constant percentage rate
`r` each year, then

`P(t)=P_0(1+r)^t`

where
`P_0` is the initial value,
`r` is expressed as a decimal, and
`t` is time in years.

This function is known as an exponential growth function.

We know that the initial value is 30 and it is increasing at a rate of 13% per year. Therefore, using the above definition we get that,

`P_0=30\\r=0.13`

`P(t)=30(1+0.13)^t=30(1.13)^t`