I'm not sure if I got the answer correct for this or not? Help please?

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?

Question

I'm not sure if I got the answer correct for this or not? Help please?

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?

lerenstudy · Answer

Answer choices are:
$$f(x)=582(7^{1/6})^{6x}$$
$$f(x)=52(7)^{x}$$
$$f(x)=582(7^{12})^{x/12}$$
$$f(x)=5852(7)^x$$

lerenstudy · Answer

I think it's the last one but I'm not sure

anonymous · Answer

Well, two months is $1/6$th of a year.

lerenstudy · Answer

right, so then the first one would be true?

anonymous · Answer

Yes

lerenstudy · Answer

And then the x/12 would work because you could replace x with 2 correct?

anonymous · Answer

Wait, let me think about it for a second

anonymous · Answer

Are you sure those are the answers?

lerenstudy · Answer

Yes, I just checked them over now

anonymous · Answer

The first one is the one that seems to make the most sense, I guess

lerenstudy · Answer

Right, but I have to eliminate all possible answers and find the one that doesn't work

lerenstudy · Answer

And the most random seems to be the final one

seratul · Answer

Maybe this could help. http://openstudy.com/updates/52ab9f5ae4b0b09acc7ee460

lerenstudy · Answer

^I looked at that but they're saying which one works, I think. I need the one that doesn't

lerenstudy · Answer

My logic right now on picking the last one is that the starting number wouldn't be more, would it?

lerenstudy · Answer

oh is CORRECT for the situation. That's such a weird phrasing. So then it would be the first one

anonymous · Answer

You should pick the ans. that will give the same results some length of time, say a year.  so $$582*7^1 = ?$$

anonymous · Answer

can also check results for two months $$582*7^{(1/6)} = ??$$

lerenstudy · Answer

So the first would be 4109 and the second would be approx 805

anonymous · Answer

compare the one year formulation to the 2 month one $$582*(7^{1/6})^6 = 582*7^1$$

anonymous · Answer

six two months = 1 year

anonymous · Answer

wait! that doesn't make sense

lerenstudy · Answer

Right, they're not the same and that wouldn't work out, so would it be the third one, because otherwise you're just making it into a year again, right?

anonymous · Answer

the first and third are the same... for time in units of two months you would want $$582*(7^{1/6})^t$$ which isn't an option?

lerenstudy · Answer

It's not

lerenstudy · Answer

I think maybe the x/12 wasn't an exponent. It's really hard to tell from what they gave me

anonymous · Answer

None of the others work... humm.

anonymous · Answer

you would need the x in an exponent.

lerenstudy · Answer

So then the first, because otherwise they would be the same?

anonymous · Answer

$$582*(7^{1/6})^{6x}=582*7^{6x/6}=582*7^x$$

anonymous · Answer

so the units x is in are still years.

anonymous · Answer

So idk what they want.

lerenstudy · Answer

right but just saying 2/12th of the final answer would be wrong, right?

lerenstudy · Answer

I'll just go through with the first and see if it comes out right or wrong

anonymous · Answer

it looks like the best bet.

lerenstudy · Answer

It said it was right, so I guess that works out

anonymous · Answer

I still don't buy it. but good it accepted it. :)

lerenstudy · Answer

Yup, thanks a lot still. I mean, that whole question was worded weird but we somehow managed to at least get it right

anonymous · Answer

np.