Question

The function f(x) = 396(3)x represents the growth of a dragonfly population every year in a remote swamp. Pierre wants to manipulate the formula to an equivalent form that calculates every month, not every year. Which function is correct for Pierre's purposes?

Answer 1

F(x)= 396 x (3 1/12) 12x

Answer 2

Answer:

The require function is $f(x)= 396(\frac{7}{6})^{12x}$ represents the growth of a dragonfly in every months.

Step-by-step explanation:

Given : The function $f(x) = 396(3)^x$ represents the growth of a dragonfly population every year in a remote swamp.

To find : The function represent the growth every month.

Solution :

Let x represents the number of years.

In 1 year there is 12 months

In x years there is 12x months  

The given function is in exponential form $y=a(1+r)^x$

where, a is initial value,  r is growth rate , (1+r) is growth rate factor

Comparing the given equation with general form

$f(x) = 396(3)^x$

$y = 396(1+2)^x$ growth of dragonfly every year

To convert into months time is multiply with 12 and growth rate is divisible by 12.

$y = 396(1+\frac{2}{12})^{12x}$

$y = 396(\frac{7}{6})^{12x}$

Therefore, The require function is $f(x)= 396(\frac{7}{6})^{12x}$ represents the growth of a dragonfly in every months.