# Find the outside temperature?

1. Jan 12, 2015

### Math10

1. The problem statement, all variables and given/known data
A cup of boiling water is placed outside at 1:00 PM. One minute later the temperature of the water is 152 degrees Fahrenheit. After another minute its temperature is 112 degrees Fahrenheit. Find the outside temperature.

2. Relevant equations
None.

3. The attempt at a solution
T(t)=Ta+(To-Ta)e^(-kt)
T(t)=Ta+(212-Ta)e^(-kt)
T(1)=152=Ta+(212-Ta)e^(-k)
T(2)=112=Ta+(212-Ta)e^(-2k)
152-Ta=(212-Ta)e^(-k)
112-Ta=(212-Ta)e^(-2k)
112/152=e^(-k)
e^k=152/112
k=ln(19/14)
Now I'm stuck. What do I do?

2. Jan 12, 2015

### ehild

That is wrong. Correctly: $\frac{112-T_a}{152-T_a}=e^{-k}$
Substituting the exponent into the first equations eliminates the unknown k:

$152-Ta=(212-Ta)\frac{112-T_a}{152-T_a}$

Solve for Ta.

3. Jan 13, 2015

### Math10

Thank you so much for the help! I got the right answer!

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