Question

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

Answer:f(x)=582(7^1/6)^6x

Explanation:

i took the test

Answer 2

Answer: The required function is,

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

Explanation:

Since, the population which is increasing with the constant factor is,

`P(x)=ab^x`

Where, a is the initial population,

b is the growth factor per period,

x is the number of periods.

Here, the given function that represents the mosquito population after x years,

`f(x)=582(7)^x`

Where, 7 is the growth factor per year,

Since, 12 months = 1 year,

2 month = 1/6 year.

Also, we can write,

`582(7)^x=582(7)^{(1)/(6)* 6x}=582(7^(1)/(6))^(6x)`

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

Which is the required equivalent function that shows the population of mosquito is increasing in every 2 month by the growth factor
`7^(1)/(6)`.