The temperature in a room is 21 degrees Celsius. A thermometer which has been kept in it is placed outside. After 5 minutes the thermometer reading is 16 Celsius. Five minutes later, it is 13 Celsius. Find the outside temperature.

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- September 6th 2007, 08:35 AMfriend37866[SOLVED] Exponential models
The temperature in a room is 21 degrees Celsius. A thermometer which has been kept in it is placed outside. After 5 minutes the thermometer reading is 16 Celsius. Five minutes later, it is 13 Celsius. Find the outside temperature.

- September 6th 2007, 08:52 AMtopsquark
This is related to Newton's Law of Cooling, I presume. (See part way down the page of this link.)

We have that

where is the temperature of the body (in this case the thermometer), is the temperature of the environment, and is the "time constant," which we don't know yet.

We know that and that at , , and at , .

So:

and

Two equations and two unknowns. We want and don't care about the time constant, so what I recommend you do is, instead of trying to solve for directly, solve the top equation for . Then note that and use that for your substitution. You'll be left with an equation for .

Sorry, I gotta run.

-Dan