Problem Solving

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

A.65
B.75
C.80
D.85
E.90

Ans:B.75

T = 120(2^-at)+60
120 = 120 (2^(-10a)) + 60
-10a = -1 or a=1/10
thus for 30 min,
at = 3 or -at = -3
thus temp = 120 (2^ (-3)) + 60
120/8 + 60 = 75
IMO B

How did you get -10a = -1 or a=1/10 ??

Thanks a ton!

B it is

with 10 mins your formula will look like
120=120(2^-10a) +60
60=120(2^-10a)
60=120 * 1/2^10a
60/120=1/2^10a
1/2=1/2^10a
2^10a=2
a=1/10
Hope this helps