Chapter 9.1, Problem 5MP

(A)

To determine

To show: The price function $p\left(t\right)=25-C{e}^{-0.2t}$ is the general solution of the differential equation $\frac{dp}{dt}=5-0.2p;t\ge 0$ and evaluate the equilibrium price $\overline{p}$.

(B)

To determine

To graph: The particular solutions satisfying the initial conditions $p\left(0\right)=40$, $p\left(0\right)=5$ and $p\left(0\right)=25$.

(C)

To determine

To discuss: The long-term behavior of the price of the product.