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?

Question

anonymous · Answer

A. f(x)= 33(3)^x
b. F(x)=396(3^12)x/12
C. f(x)=396(3^1/12)^12x
D. f(x)=4752(3)^x

anonymous · Answer

So, I got C?

irishboy123 · Answer

**absent typos**: $\large 396(3^{\frac{1}{12}})^{12x} = 396(3^{\frac{1}{12} \times 12x}) = 396(3)^{x}$ ie back to where you started. plug a number in and see. none of these look right https://gyazo.com/5b74d0c9b3753f89f9467f1bc3f2858c

irishboy123 · Answer

screenshot?

anonymous · Answer

@campbell_st

anonymous · Answer

f(x) = 33(3)x

 f(x) = 396(312)the x over 12 power

 f(x) = 396(3 to the one twelfth power)12x

 f(x) = 4752(3)x

campbell_st · Answer

this is the 2nd time I have seen one of these questions and they don't make much sense to me... 

I'd expect for this exponential model if the time changes to months the value of x
needs to be divided by 12

so you can test by looking at 

the model 

$$f(1) = 396(3)^{\frac{1}{12}}$$

then find f(2) and f(3) to see if there is growth

hope it helps

anonymous · Answer

That"s not an answer choice:( @campbell_st

campbell_st · Answer

well remember the index law for power of a power, multiply the powers

$$(x^a)^b = x^{a \times b}$$

so you have 

$$3^{\frac{x}{12}} = (3^?)^x$$

anonymous · Answer

12?

anonymous · Answer

So would I be right when I said, C?