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 answer is C

Because: (1.04)^4 = 1.1699

Answer 2

For this case we have the following exponential function:

`f (x) = 40 (1.04) ^ {4x}`
By power properties we can rewrite this function.
We have then that the equivalent expression is:

`f (x) = 40 ((1.04) ^ 4) ^ x`
Rewriting we have:

`f (x) = 40 (1.1699) ^ x`
Answer:
the following is an equivalent function
c. f (x) = 40 (1.1699) x