Question

The function f(x) = 15(2)x represents the growth of a frog population every year in a remote swamp. Elizabeth wants to manipulate the formula to an equivalent form that calculates every half-year, not every year. Which function is correct for Elizabeth's purposes? f(x) = 15(2 to the one half power)2x f(x) = 15(22)the x over 2 power f(x) = fifteen halves(2)x f(x) = 30(2)x

Answer 1

Answer :
`f(x)=15(2^(1)/(2))^(2x)`

The function
`f(x)= 15(2)^x` represents the growth of a frog population every year in a remote swamp.

Elizabeth calculates every half year. so 2 times a year.

x years will becomes 2x years. We also need the raise 2 inside the parenthesis to the exponent 1/2

So the function becomes
`f(x)=15(2^(1)/(2))^(2x)`