GMATPrep exponents question

[allenkt]

I ran into a question on the GMAT prep that I've seen before but I can't seem to find it so I can see how to solve it. I didn't write down the exact question but it was one about figuring out the temperature of a cup of coffee 30 minutes after is was poured given the temp at 10 minutes and a formula.

The formula, where F = temperature and t = minutes after is was poured and a = some constant is:

F = 120 (2^-at) + 60

So I'm given F = 120 at t = 10 then I need to figure out F at t = 30. Seems simple enough but for the life of me I don't know what to do with the 'a' exponent. I can get as far as 1 / 2^10a but I can't figure out where to go next to solve for a. Help!

[jayhawk2001]

I ran into a question on the GMAT prep that I've seen before but I can't seem to find it so I can see how to solve it. I didn't write down the exact question but it was one about figuring out the temperature of a cup of coffee 30 minutes after is was poured given the temp at 10 minutes and a formula.

The formula, where F = temperature and t = minutes after is was poured and a = some constant is:

F = 120 (2^-at) + 60

So I'm given F = 120 at t = 10 then I need to figure out F at t = 30. Seems simple enough but for the life of me I don't know what to do with the 'a' exponent. I can get as far as 1 / 2^10a but I can't figure out where to go next to solve for a. Help!

For t=10,

120 = 120*(2^-at) + 60
1/2 = 2^-at
2^-at = 2^-1
at = 1
a = 1/10 (at t=10)

Using this for t=30

F = 120*(2^-30/10) + 60
= 120*2^-3 + 60
= 15 + 60
= 75

[allenkt]

Everything makes sense except for one part.

2^-at = 2^-1
then
at = 1

So are you saying that if X^a = X^b, then a = b?

Ok, never mind, writing it like that I now see it. If the bases are the same and the values are the same, then the exponents must also be equal. That is the step I couldn't see when trying to solve this.

Thanks!