Question

HOW TO GET THE ANSWER??
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?

f(x) = 582(7 to the one sixth power)6x

f(x) = 52(7)x

f(x) = 582(712)the x over 12 power

f(x) = 5852(7)x

Answer 1

HELP!

Answer 2

oh is that \(\large f(x)=5852(7)^x\)

Answer 3

d?

Answer 4

no sorry I was just confused about your notation

Answer 5

yeah but you mean 582*

Answer 6

is it c?

Answer 7

It looks like a) should be right but I'm not sure of the formatting of the answer. But really if :
\[x = \text{1 year}\]
then
\[\frac{x}{12}=\text{1 month}\], so \[\frac{2x}{12}=\frac{x}{6}=\text{2 months} \]

Answer 8

So just go with a?

Answer 9

i think so

Answer 10

thank you!

Answer 11

:)

Answer 12

\[f(x)=582*7^x = 582*(7^{1/6})^{6x}\]because \[(a^b)^c = a^{b*c}\]
Following this pattern, if we wanted a formula that worked on a daily basis, we would use \[f(x) = 582*(7^{1/365})^{365x}\]
And so on...