Chapter 1, Problem 14P

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),

$\frac{dT}{dt}=-k\left(T-T_a\right)$

where $T=$ the temperature of the body $\left(\text{°C}\right),t=$ time (min), $k=$ the proportionality constant (per minute), and $T_a=$ the ambient temperature $\left(\text{°C}\right)$. Suppose that a cup of coffee originally has a temperature of $70°\text{C}$. Use Euler's method to compute the temperature from $t=0$ to 10 min using a step size of 2 min if $T_a=20°\text{C}$ and $k=0.019\text{/min}$.