Question

The function f(x) = 245(4)x represents the growth of a fruit fly population every year in the orange grove. Stacey wants to manipulate the formula to an equivalent form that calculates every month, not every year. Which function is correct for Stacey's purposes?

Answer 1

Answer:
`f(x) =245(1.25)^(12x)`

Explanation:

Since, The function that shows the growth of fruit fly population every year is,

`f(x) =245(4)^(x)`

⇒
`f(x) =245(1+3)^(x)`

Where 3 is the annual growth rate and x is number of years (time).

If he want to calculate the growth of the fly in every month then

The total time = 12x

Monthly growth rate =
`(3)/(12) = 0.25`

Thus, the total growth of the fruit fly after x years,

`f(x) =245(1+0.25)^(12x)`

⇒
`f(x) =245(1.25)^(12x)`

Which is the required function.