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 (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. supermarkets 5000 By hand, sketch a solution curve of the given initial-value problem. N 4000 3000 2000 = N(1 0.0002N), N(0) = 1. 1000 O 5 10 15 N 2500 VILL 2000 1500 1000 500 5 10 20 N 5000 4000 3000 2000 0 1000 5 10 15 (b) Solve the initial-value problem and then use a graphing utility to verify the solution curve in part (a). N(t) = 20 How many supermarkets are expected to adopt the new technology when t= 10? (Round your answer to the nearest integer.) supermarkets 15 20 t N 2500 2000 1500 1000 500 5 10 15 20 t Ⓡ

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