# Math Help - Cooling problem

1. ## Cooling problem

A thermometer is taken from a room temperature 22degreesC and placed outside where the temperature is -10degreesC. One minute later, the thermometer reads 10degreesC. Use Newton's law of cooling to find the temperature T of the thermometer after t minutes.

2. Originally Posted by calculuskid1
A thermometer is taken from a room temperature 22degreesC and placed outside where the temperature is -10degreesC. One minute later, the thermometer reads 10degreesC. Use Newton's law of cooling to find the temperature T of the thermometer after t minutes.
Newton's law of cooling says that the rate of temperature change of an object is directly proportional to the difference between the object's temperature and the temperature of its environment.

$\frac{dT}{dt} = k[T - (-10)]$

separate variables, integrate, and get temperature, $T$ , as a function of time, $t$ .