The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem

dN/dt = N(1 - 0.0005N), N(0) = 1.

(a) Use the phase portrait concept of Section 2.1 to predict how many supermarkets are expected to adopt the new procedure over a long period of time. By hand, sketch a solution curve of the given initial-value problem.

(b) Solve the initial-value problem and then use a graphing utility to verify the solution curve in part (a). How many companies are expected to adopt the new technology when t = 10?