Temp- Gmat prep

[dilip]

Please solve this one.

The Temprature of a cetain cup of coffee 10 min after it was poured was 120 degree faheranite. If the Temp F of the cofee t minutes after it was poured can be determined by the formula F=120(2^-at)+60 , where F is in degree faheranite and a is a constant,then the Temp. of the cofee 30 min. after it was poured was how many degree Fahternite.

Ans is: 75

[RonPurewal]

hi - when you list problems, you should make a habit of listing the COMPLETE PROBLEM, including answer choices. the answer choices are often crucial in attacking the problem - some problems, especially hard problems, can be attacked using "back door" techniques that take advantage of the answer choices, rather than traditional problem solving techniques.

for this problem, though, there's not really any easy way to use the answer choices to your advantage, so we'll go for it.

first, use the GIVEN information, which is that F = 120 when t = 10.
therefore, 120 = 120(2^-10a) + 60
60 = 120(2^-10a)
1/2 = 2^-10a
-1 = -10a (note that you have to realize that 1/2 is 2^-1; you may want to review negative exponents at this point if you can't make this realization)
a = 1/10

this "a" is a constant, so we can now substitute it into the problem, giving the complete formula: F = 120(2^-t/10) + 60.
now plug in 30:
F = 120(2^-30/10) + 60
= 120(2^-1/3) + 60
= 120(1/8) + 60 (note that you again need a decent amount of facility with negative exponents)
= 15 + 60
= 75

there you go