Question

50 POINTS...!!!! The function f(x) = 582(7)^x represents the growth of a mosquito population every year in a remote swamp. Troy wants to manipulate the formula to an equivalent form that calculates every 2 months, not every year. Which function is correct for Troy's purposes?

Answer 1

The answer is f(x)=582(71/6)6x

Explanation:

Answer 2

`f(x)=582(7^(1)/(6) )^(6x)` calculates the growth of a mosquito population every 2 months in a remote swamp.

Explanation:

Given : The function
`f(x) = 582(7)^x` represents the growth of a mosquito population every year in a remote swamp.

We have to manipulate the formula to an equivalent form that calculates every 2 months.

Since, the function in growth model is given by

`f(x)=a(1+r)^n`

Where a is initial amount

and r is rate of increase

and n is time

Since, now the population is calculated after every 2 months that is

In 1 year, it is calculated 6 times.

So, We multiply the time by 6 and rate factor is divided 6 times .

So, the function now becomes,

`f(x)=582(7^(1)/(6) )^(6x)`

Thus,
`f(x)=582(7^(1)/(6) )^(6x)` calculates the growth of a mosquito population every 2 months in a remote swamp.