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# The temperature of a cup of coffee 10 minutes after it was

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Intern
Joined: 09 Jun 2006
Posts: 14
The temperature of a cup of coffee 10 minutes after it was [#permalink]

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03 Oct 2006, 17:43
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

The temperature of a cup of coffee 10 minutes after it was poured was 120 degrees F. If the temp (F) of the cup of coffee t minutes after it was poured can be determined by F=120(2^(at)) + 60 , where a is a constant, then what was the temperature 30 minutes after it was poured?
Manager
Joined: 25 May 2006
Posts: 227

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03 Oct 2006, 19:12
F=120(2^(at)) + 60

120=120(2^(a10)) + 60
1/2=2^(a10)
1/2=1/2^(-a10) ---> so we need that (-a*10)=1 so a=-1/10

For 30 min
F=120(2^((-1/10)*30)) + 60
F=120*(1/2^3)+60
F=15+60
F=75
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Senior Manager
Joined: 14 Jul 2005
Posts: 402

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04 Oct 2006, 13:39
Got 75 also .. same working as X&Y
Manager
Joined: 31 Aug 2006
Posts: 210

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04 Oct 2006, 13:59
Same answer.For simplifying the working process,I converted the minutes into hrs.Hence I assumed t=1/6 where t=10 and t=1/2 where t=30.This gives a=-6.Using this I get F=75.
Director
Joined: 23 Jun 2005
Posts: 841
GMAT 1: 740 Q48 V42

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04 Oct 2006, 14:45
120 = 120(2^(10a))+60
Simplifying,
2^-1 = 2^10a
a= -1/10

After 30 minutes,

F = 120 (2^-3)+60
= (120/8)+60
F=75
Senior Manager
Joined: 30 Aug 2006
Posts: 374

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04 Oct 2006, 15:24
same as above, 75.

a = -1/10

after 30 mins:

120(2^(-1/10 * 30)) + 60
120(2^-3) + 60
120(1/8) + 60
15 + 60
75
SVP
Joined: 05 Jul 2006
Posts: 1747

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04 Oct 2006, 16:37
The temperature of a cup of coffee 10 minutes after it was poured was 120 degrees F. If the temp (F) of the cup of coffee t minutes after it was poured can be determined by F=120(2^(at)) + 60 , where a is a constant, then what was the temperature 30 minutes after it was poured?

F=120(2^(at)) + 60

GET A

120-60=60/120 = 1/2 = 2^-1

10A = -1 THUS A = -1/10

F= 1/8(120) +60 = 75
Intern
Joined: 09 Jun 2006
Posts: 14

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04 Oct 2006, 17:24
75 is correct, thanks a lot guys.
04 Oct 2006, 17:24
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