Chapter 10.1, Problem 19E

Rate of Net Investment Let $f\left(t\right)$ denote the amount of capital invested by a certain business firm at time $t$. The rate of change of invested capital, $f\text{'}\left(t\right)$ is sometimes called the net of investment. The management of the firm decides that the optimum level of investment should be $C$ dollars and that, at any time, the rate of net investment should be proportional to the difference between $C$ and the total capital invested. Construct a differential equation that describes this situation.