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?
a. f(x) = 40(4.1600)x
b. f(x) = 480(1.04)x
c. f(x) = 40(1.1699)x
d. f(x) = 480(4.1600)x

Answer 1

The equivalent expression is:
`40(1.1699)^x`

Hence, option c is correct.

Explanation:

We have been given the function:

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

Using:

`x^(ny)=(x^n)^y`

Here, n=4 and x=y

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

On simplification of
`1.04^4=1.1698\approx1.1699` so we get:

`40(1.1699)^x`

Therefore, the equivalent expression is:
`40(1.1699)^x`

Hence, option c is correct.