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Applications of First-order Differential Equations to Real by the linear first-order differential equation order Differential Equations to Real World Application 1 : Exponential Growth - Population Let P(t) be a quantity that increases with time t and the rate of increase is proportional to the same quantity P as follows d P / d t = k P where d p / d t is the first derivative of P, k > 0 and t is the time. The solution to the above first order differential equation is given by P(t) = A e k t

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