Temprature Problem

[mh09]

The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120 (2^-at) +60, where F is in degrees Fahrenheit and a is a constant, then the temperature of the coffee 30minutes after it was poured was how many degrees Fahrenheit?

a) 65
b) 75
c) 80
d) 85
e) 90

[Daan]

F = 120. 2^-at +60

We know that when t = 10 (min.), F = 120
Use this to determine a

120 = 120. 2^-a.10 +60
60 = 120. 2^-a.10
1/2 = 2^-a.10

We know 1/2 = 2^-1, so
2^-a.10 = 2^-1
-a.10 = -1
a= 1/10

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Now substite t=30 minutes and a=1/10 in the original equation:

F = 120. 2^-(1/10).30 +60
F = 120. 2^-3 +60

2^-3 = 1/ (2³) = 1/ (2.2.2) = 1/8

F = 120. 1/8 +60
F = 120/8 +60
F = 15 + 60
F = 75


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PS
It'd be better to post such questions in the 'Problem Solving' section.
You'll probably get a quicker response!

[xperience]

Originally Posted by mh09

The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120 (2^-at) +60, where F is in degrees Fahrenheit and a is a constant, then the temperature of the coffee 30minutes after it was poured was how many degrees Fahrenheit?

a) 65
b) 75
c) 80
d) 85
e) 90

If I am not wrong.. this problem is from Gmatprep, right..??

[mh09]

Thanks Dan ... and yes, this problem is from the GMAT prep ... more to come.