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: The required function is,

$f(x)=582(7^\frac{1}{6})^{6x}$

Step-by-step 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,

$582(7)^x=582(7)^{\frac{1}{6}\times 6x}=582(7^\frac{1}{6})^{6x}$

$\implies f(x)=582(7^\frac{1}{6})^{6x}$

Which is the required equivalent function that shows the population of mosquito is increasing in every 2 month by the growth factor $7^\frac{1}{6}$.