Question

The function f(x) = 25(4)x represents the growth of a bird population every year in a national park. Kyle wants to manipulate the formula to an equivalent form that calculates every half-year, not every year. Which function is correct for Kyle's purposes?

f(x) = 25(4)the x over 2 power
f(x) = twenty five halves(4)x
f(x) = 25(4 to the one half power)2x
f(x) = 50(2)x

Answer 1

@ganeshie8

Answer 2

\[
f(x) = 25(4)^x ~~ \text{where x is in years. }\\
\text{But now it is changed so x represents half-year. }\\
\text{So x has to be divided by 2 to convert it to a year in the original formula:} \\
\large f(x) = 25(4)^{\frac x 2}
\]