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

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28 Jul 2010, 09:11

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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?

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

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28 Jul 2010, 11:57

Hi,

Since F=120 (2^-at)+60, replace F=120, t=10 to find a. Once you find a, then to find the temperature 30 min after it was poured simply replace t=30 and value of a in the equation.

The tempreature of a certain cup of coffee 10 minutes after it was poured was 120 degree Faranite. If the temp F of the coffee t minues after it was poured can be determinde by the formula F=120 (2^-at)+60 , where F is degree Fahrenhite and a is constant, then the tempreature of the cofffee 30 minues after it was poured was how many degree fahrenhite

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 \(F=120*2^{-0.1*30}+60=\frac{120}{2^3}+60=75\).

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

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08 Oct 2017, 12:13

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