Chapter 10.1, Problem 31E

Technology Exercise

Consider the differential equation $y\text{'}=.2\left(10-y\right)$ from Example $6$. If the initial temperature of the steel rod is ${510}^{\circ }C$, the function $f\left(t\right)=10+500e^{-0.2t}$ is the solution of the differential equation.

a. Graph the function in the window $\left[0,30\right]$ by $\left[-75,550\right]$.

b. In the home screen, compute $.2\left(10-f\left(5\right)\right)$ and compare this value with $f\text{'}\left(5\right)$