# A body at a temperature of 50 ^{\circ} F is placed outdoors where the temperature is 100 ...

## Question:

A body at a temperature of 50{eq}^{\circ} {/eq} F is placed outdoors where the temperature is 100{eq}^{\circ} {/eq} F. If after 5 minutes the temperature of the body is 60{eq}^{\circ} {/eq} F, find how long it will take the body to reach a temperature of 75{eq}^{\circ} {/eq} F. Also find the temperature of the body after 20 minutes.

## Newton's Cooling (Heating) Law

Newton's Cooling (Heating) Law is an equation that describes the transfer of heat between the environment and the body. It is an exponential function that is a function of time and is explicitly given by the function {eq}T(t) = M - A e^{-kt} {/eq} where M is the temperature of the surroundings, A and k are constants related to the system being examined.

## Answer and Explanation:

In this problem we need to establish the exponential function that describes the temperature of the body. This means that we need to solve for the...

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