Question

25 POINTS!!!!!!

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?

A. f(x) = 67(5)x
B. f(x) = 467(512)the x over 12 power
C. f(x) = 467(5 to the one fourth power)4x
D. f(x) = 4672(5)x

Answer 1

Your anwer is C)f(x) = 467(5 to the one fourth power)4x

Answer 2

Answer: C.
`f(x)=467(5)^{(1)/(4)x}`

Explanation:

Given: The function
`f(x)=467(5)^x` represents the growth of a ladybug population every year in a wooded area.

If Adrianne wants to manipulate the formula to an equivalent form that calculates every 3 months, not every year.

Then, the time changes from 1 year to 3 months.

Since, 1 year = 12 months

And 1 month =
`(1)/(12)` year

So, 3 months =
`(3)/(12)=(1)/(4)` year

So, the required function would look like :_

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

Hence, C is the right answer.