Chapter 9.1, Problem 56E

a.

To determine

To show: The solution of the initial value problem is $M\left(t\right)=K{\left(\frac{M_0}{K}\right)}^{\exp \left(-rt\right)}$.

b.

To determine

To sketch: The graph of the solution $M\left(t\right)=K{\left(\frac{M_0}{K}\right)}^{\exp \left(-rt\right)}$ for $M_0=100$ and $r=0.05$.

c.

To determine

To evaluate: The value of $\underset{t\to \infty }{\lim }M\left(t\right)$ by using the graph in part (b).