Question

Which of the following is an equivalent function to the function below? f(x) = 30(1.03)3x f(x) = 30(3.0900)x f(x) = 30(1.0927)x f(x) = 10(1.0927)x f(x) = 10(3.0900)x

Answer 1

Given function : $f(x) = 30(1.03)^{3x}$.

We need to find the equivalent function to the given function.

$30(1.03)^{3x}$ could be written as $30(1.03^3)^{x}$.

$1.03^3=1.092727$

So, we can round 1.092727 to 1.0927.

Replacing 1.03^3 by 1.0927 in $30(1.03^3)^{x}$, we get

$f(x) = 30(1.0927)^{x}$.

Therefore, f(x) = 30(1.0927)^{x} is an equivalent function to the $f(x) = 30(1.03)^{3x}$.