Question

The function f(x) = 467(5)x represents the growth of a ladybug population every year in a wooded area. Adrianne wants to manipulate the formula to an equivalent form that calculates every 3 months, not every year. Which function is correct for Adrianne's purposes?

Answer 1

f(x)=467(5^1/4)^4x is the closest I can get.

Answer 2

The function is
`f(x)=467((5)^{(1)/(4)})^(4x)`

Explanation:

We are given that,

The function representing the growth of ladybug population every year is,

`f(x)=467(5)^x`, where x= number of years.

Adrianne wants to calculate the population after every 3 months.

Since, 12 months = 1 year

i.e. 1 month =
`(1)/(12)` years

i.e. 3 month =
`(3)/(12)=(1)/(4)` years.

Then the new function showing the population after every 3 months will be,

`f(x)=467(5)^{(1)/(4)* 4x}`

i.e.
`f(x)=467((5)^{(1)/(4)})^(4x)`

Hence, the required function is
`f(x)=467((5)^{(1)/(4)})^(4x)`