Chapter 28, Problem 42P

The rate of cooling of a body can be expressed as

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

where $T=$ temperature of the body $\left(°\text{C}\right)$, $T_a=$ temperature of the surrounding medium $\left(°\text{C}\right)$, and $k=$ the proportionality constant (min^-1). Thus, this equation specifies that the rate of cooling is proportional to the difference in temperature between the body and the surrounding medium. If a metal ball heated to $90°\text{C}$ is dropped into water that isheld at a constant value of $T_a=20°\text{C}$, use a numerical method tocompute how long it takes the ball to cool to $40°\text{C}$ if $k=0.25{\text{ min}}^{-1}$.