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# The temperature of a certain cup of coffee 10 minutes after

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Manager
Joined: 27 May 2007
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The temperature of a certain cup of coffee 10 minutes after [#permalink]

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12 Aug 2007, 12:45
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Difficulty:

15% (low)

Question Stats:

81% (01:33) correct 19% (01:34) wrong based on 417 sessions

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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 30 minutes after it was poured was how many degrees Fahrenheit?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-temperature-of-a-certain-cup-of-coffee-10-minutes-after-98165.html
[Reveal] Spoiler: OA

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Director
Joined: 30 Jun 2007
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Re: The temperature of a certain cup of coffee 10 minutes after [#permalink]

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12 Aug 2007, 14:56
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The temperature of coffee 10 minutes after it was poured (120 F) will help in solving the constant “a”.
120 = 120(2 ^ 10a) + 60
2 ^ -1 = 2 ^ 10a
a = -1/10
The temperature of coffee 30 minutes after it was poured is:
F = 120 ( 2 ^ -30/10) + 60
F = 120 * 1/ 8 + 60
F = 15 + 60
F = 75

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Manager
Joined: 27 May 2007
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Re: The temperature of a certain cup of coffee 10 minutes after [#permalink]

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12 Aug 2007, 15:33
You're right - OA is B.

When I see a problem that looks this complex, and I'm being timed, I think my brain freezes. Seriously, it's hard to think straight and just plow through it. I'm worried about how much time it will take to solve, and should I spend that much time, etc. Less than a week to go, I really need to get my speed up.

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Re: The temperature of a certain cup of coffee 10 minutes after [#permalink]

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25 Sep 2014, 16:55
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Re: The temperature of a certain cup of coffee 10 minutes after [#permalink]

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26 Sep 2014, 00:10
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Robin in NC wrote:
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 30 minutes after it was poured was how many degrees Fahrenheit?

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

We have the formula for calculating temperature: $$F=120*2^{-at}+60$$ and the value for $$t=10$$ --> $$F(t=10)=120=120*2^{-10a}+60$$ --> $$\frac{1}{2^{10a}}=\frac{1}{2}$$ --> $$10a=1$$ --> $$a=0.1$$. So formula is $$F=120*2^{-0.1t}+60$$

Now for $$t=30$$ the temperature in Fahrenheits will be $$F=120*2^{-0.1*30}+60=\frac{120}{2^3}+60=75$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-temperature-of-a-certain-cup-of-coffee-10-minutes-after-98165.html
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Kudos [?]: 128668 [6], given: 12181

Re: The temperature of a certain cup of coffee 10 minutes after   [#permalink] 26 Sep 2014, 00:10
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