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## Homework Statement

At 1:00PM, a thermometer reading 70

^{o}F is taken outside where the air temperature is -10

^{o}F. At 1:02PM, the reading is 26

^{o}F. At 1:05PM, the thermometer is taken back indoors, where the air is at 70

^{o}F. What is the temperature reading at 1:09PM?

## Homework Equations

## The Attempt at a Solution

At t=0, u=70F, temp.env.=-10F

At t=2, u=26F.

At t=5 u=? env=70F

At t=9, u=?

[itex]\frac{du}{dx}=k(u+10)[/itex]

u+10=ce

^{kt}

at t=0, c=80F

u+10=80e

^{kt}

at t=2, u=26, k=-0.39925

Giving me the u value which is 0.86729

After that, I don't know what to do next. :|

I actually tried letting u=0.86729 and k=-0.39925 when t=0. And after doing the same process, I ended up having u=60.608F but the answer should be 58F.

Is there any shortcut or pattern in obtaining the answer to this kind problems?