1. The number N(t) of supermarkets throughout the country thatare using a computerized checkout system is described by theinitial-value problemdN/dt = N(1 - 0.0005N), N(0) = 1.(a) Use the phase portrait concept of Section 2.1 to predicthow many supermarkets are expected to adopt the newprocedure over a long period of time. By hand, sketch asolution curve of the given initial-value problem.(b) Solve the initial-value problem and then use a graphingutility to verify the solution curve in part (a). How manycompanies are expected to adopt the new technology whent = 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.