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Suppose the population P of rainbow trout in a fish hatchery is modeled by the differential equation dP F3 = P(6 — P), where P is measured in thousands of trout and ¢ is measured in years. Suppose P(0) = 1. (a) How many trout are initially in the hatchery? EOOO } trout. (b) Find a formula for the population at any time. 3 thousands of trout. (c) What is the size of the trout population after a very long time? lim P(t) = 0 thousands of trout. t—o0 - (d) At what time is the trout population increasing most rapidly? t = &.268 } years.