Question

The function f(x) = 20(3)x represents the growth of a fish population every year in a local lake. Jesse wants to manipulate the formula to an equivalent form that calculates every half-year, not every year. Which function is correct for Jesse's purposes? f(x) = 20(3)the x over 2 power f(x) = 20(3 to the one half power)2x f(x) = twenty halves(3)x f(x) = 40(2)x

Answer 1

In the equation, 20 is the original number of fish so we do not change that value to compensate for growth every half year. We will have to change the rate of growth, i.e, 3 and bring 1/2 into its power,
f(x) = 20(3)^(x/2) is correct

Answer 2

One year is represented by x. Therefore, half year would be represented by $\frac{x}{2}$. Now just substitute x with $\frac{x}{2}$ in the formula $y=20(3)^x$.

$y=20(3)^{ \frac{x}{2} }$