# Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between

###### Question:

Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature), $$\frac{d T}{d t}=-k\left(T-T_{a}\right)$$ where $T=$ the temperature of the body $\left(^{\circ} \mathrm{C}\right), t=$ time $(\mathrm{min}), k=$ the proportionality constant (per minute), and $T_{a}=$ the ambient temperature $\left(^{\circ} \mathrm{C}\right)$. Suppose that a cup of coffee originally has a temperature of $68^{\circ} \mathrm{C}$. Use Euler's method to compute the temperature from $t=0$ to 10 min using a step size of 1 min if $T_{a}=21^{\circ} \mathrm{C}$ and $k=$ $0.017 / \mathrm{min}$.

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