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

Answer:

The function is $f(x)=467((5)^{\frac{1}{4}})^{4x}$

Step-by-step 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 = $\frac{1}{12}$ years

i.e. 3 month = $\frac{3}{12}=\frac{1}{4}$ years.

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

$f(x)=467(5)^{\frac{1}{4}\times 4x}$

i.e. $f(x)=467((5)^{\frac{1}{4}})^{4x}$

Hence, the required function is $f(x)=467((5)^{\frac{1}{4}})^{4x}$