# 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.

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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