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The temperature of a certain cup of coffee 10 minutes after

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The temperature of a certain cup of coffee 10 minutes after [#permalink] New post 12 Nov 2006, 00:16
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The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenhheit. 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 he temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit?

65
75
80
85
90
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 [#permalink] New post 12 Nov 2006, 03:27
By plugging in 120 and 10 and solving, you can find that 2^(-10a)=1/2

For 30 minutes, substitute 30 for 10 so, 2^(-30a) which is (2^-10a)^3

which is (1/2)^3

So going back to the original equation

F=120(1/8)+60 = 75

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 [#permalink] New post 12 Nov 2006, 08:59
Anyone else want to try before I give the OA?
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 [#permalink] New post 12 Nov 2006, 09:11
I got 75 also.

plugging the numbers a = 1/10, and when we substitute 30 for T, the temperature comes to 75.
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 [#permalink] New post 12 Nov 2006, 09:18
Yep. OA is 75 :P
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  [#permalink] 12 Nov 2006, 09:18
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