Question

The expression below shows the population of butterflies in a forest after 4x years: f(x) = 40(1.04)^4x Which of the following is an equivalent function? f(x) = 40(4.1600)^x f(x) = 480(1.04)^x f(x) = 40(1.1699)^x f(x) = 480(4.1600)^x

Answer 1

(1.04)^4 = 1.1699

so the correct choice is the third one.

Answer 2

`f(x)= 40(1.1699)^x`

Explanation:

The expression below shows the population of butterflies in a forest after 4x years.

`f(x)=40(1.04)^(4x)`

To find out the equivalent function, we need to multiply the exponent 4 inside the parenthesis.
`(a)^m = a^m`

In the give
`(1.04)^4= 1.16985856`n function,

`(1.04)^4= 1.1699`

So f(x) becomes
`f(x)= 40(1.1699)^x`