How to solve w/o calculator? (temp of cooling coffee)

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mcheytan

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Jan 25, 2008
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The temperature in Fahrenheit (F) of a coffee 10 min after it has been poured is 120F. The temperature of that coffee at time T is found using the formula F=120( 2^(-a*T) )+60. What is F when T=30 min????

I have the following problem: I should not use calculator.
(a) is a constant
I know I can find it when I plug in the given F at 10 min after poured...but how do I find (a) without calculator.
Is there any way I can solve this without finding (a)
 
Re: How to solve w/o calculator?

\(\displaystyle 2^{-60a}\;=\;\left(2^{-10a}\right)^{6}\)?
 
Re: How to solve w/o calculator?

why would you use T=60 in the power...we need 30 min. and I need to find the temperature....?
 
Re: How to solve w/o calculator?

mcheytan said:
The temperature in Fahrenheit (F) of a coffee 10 min after it has been poured is 120F. The temperature of that coffee at time T is found using the formula F=120( 2^(-a*T) )+60. What is F when T=30 min????

I have the following problem: I should not use calculator.
(a) is a constant
I know I can find it when I plug in the given F at 10 min after poured...but how do I find (a) without calculator.
Is there any way I can solve this without finding (a)
Click to expand...
Another way - through finding 'a' first

10 min after it has been poured is 120F

\(\displaystyle 120\, = \, 120 \cdot 2^{-a\cdot 10} + 60\)

\(\displaystyle \frac{1}{2}\, = \, 2^{-a\cdot 10}\)

\(\displaystyle - 1\, = \, - 10 a\)

What is F when T=30 min????

\(\displaystyle F\, = \, 120 \cdot 2^{(-\frac{1}{10} \cdot 30)} + 60\)

\(\displaystyle F\, = \, 120 \cdot \frac{1}{8} + 60\)
 
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