# Find the outside temperature?

• Math10

## Homework Statement

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.

None.

## 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?

## Homework Statement

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.

## 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)
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.

• Math10
Thank you so much for the help! I got the right answer!