Question

The function f(x) = 4(2)x represents the growth of a butterfly population every year in a remote swamp. Jan wants to manipulate the formula to an equivalent form that calculates five times a year, not just once a year. Which function is correct for Jan's purpose, and what is the new growth rate?

Answer 1

The question ask to find and choose among the following choices the best function that is correct for Jan's purpose and the new growth rate and the best function would be letter f(x)=4(1.15)5x, growth rate is 15%. I hope you are satisfied with my answer and feel free to ask for more 

Answer 2

Answer:
`f(x)=4(1.2)^(5x)`

Explanation:

Here, The function that shows the number of butterfly,

`f(x) = 4(2)^x` or
`f(x) = 4(1+1)^x`

Where x is the number of years.

4 is the initial number of butterfly,

1 is the annual growth rate.

⇒ If the rate is calculate 5 times in a month,

Then the rate per 5 times a year = 1/5 = 0.2

And, the total number of periods in x years = 5x

Thus, the number of butterfly in x years,

`f(x) = 4(1+0.2)^(5x)`

Which is the required formula.