Answer:
The function is [tex]f(x)=467((5)^{\frac{1}{4}})^{4x}[/tex]
Step-by-step explanation:
We are given that,
The function representing the growth of ladybug population every year is,
[tex]f(x)=467(5)^x[/tex], where x= number of years.
Adrianne wants to calculate the population after every 3 months.
Since, 12 months = 1 year
i.e. 1 month = [tex]\frac{1}{12}[/tex] years
i.e. 3 month = [tex]\frac{3}{12}=\frac{1}{4}[/tex] years.
Then the new function showing the population after every 3 months will be,
[tex]f(x)=467(5)^{\frac{1}{4}\times 4x}[/tex]
i.e. [tex]f(x)=467((5)^{\frac{1}{4}})^{4x}[/tex]
Hence, the required function is [tex]f(x)=467((5)^{\frac{1}{4}})^{4x}[/tex]
