The following differential equations for the production of a chemical P share the properties that the rate of change at t = 0 is 5.0, and the limit as t → ∞ is 0. For each, find the solution starting from the initial condition P(0) = 0, sketch the solution, and say what happens to P(t) as t → ∞. Compute P(10) and P(100). Why do some increase to infinity while others do not?

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dP 5.0 dt (1+1)2