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**HallsofIvy** With N(t) as the number produced per day after t days, the "rate of change of performance w.r.t. time." is dN/dt. We are told that is "proportional to 30-N". dN/dt= k(30- N) where k is the "constant of proportion".

Write that equation as dN/(30- N)= kdt and integrate. There will be one constant of integration. Use the fact that there is a "new employee who produced 10 units on the first day at the factory and 19 units on the twentieth day" to determine both that constant and k.