Respuesta :
Answer:
[tex]f(x)=582(7^\frac{1}{6} )^{6x}[/tex] calculates the growth of a mosquito population every 2 months in a remote swamp.
Step-by-step explanation:
Given : The function [tex]f(x) = 582(7)^x[/tex] 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
[tex]f(x)=a(1+r)^n[/tex]
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,
[tex]f(x)=582(7^\frac{1}{6} )^{6x}[/tex]
Thus, [tex]f(x)=582(7^\frac{1}{6} )^{6x}[/tex] calculates the growth of a mosquito population every 2 months in a remote swamp.
