One theory on the speed an employee learns a new task claims that the more the employee already knows, the more slowly he or she learns. Suppose that the rate at which a person learns is equal to the percentage of the task not yet learned. If y is the percentage learned by time t, the percentage not yet learned by that time is 100 − y, so we can model this situation with the differential equation

(a) Find the general solution to this differential equation.
(b) Sketch several solutions.
(c) Find the particular solution if the employee starts learning at time t = 0 (so y = 0 when t = 0).

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dy dt = 100-y.