Answer: [tex]f(x) =245(1.25)^{12x}[/tex]
Step-by-step explanation:
Since, The function that shows the growth of fruit fly population every year is,
[tex]f(x) =245(4)^{x}[/tex]
⇒ [tex]f(x) =245(1+3)^{x}[/tex]
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 = [tex]\frac{3}{12} = 0.25[/tex]
Thus, the total growth of the fruit fly after x years,
[tex]f(x) =245(1+0.25)^{12x}[/tex]
⇒ [tex]f(x) =245(1.25)^{12x}[/tex]
Which is the required function.
