Question

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

Answer 1

Answer:

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

Hence, option c is correct.

Step-by-step 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.

Answer 2

Th equivalent fraction of this expression is determined by just mutiplying the constants in the original expression and see if anything fits to the new form. We multiply 1.04 by 4 to equal to 4.16 and retain the 40. Hence the answer is f(x) = 40(4.1600)x.