he 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 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

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.