Using derivatives write an equation representing the growth, Physics

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Using derivatives write an equation representing the growth

At any time, t, a population, P(t), is growing at a rate proportional to the population at that moment.

(a) Using derivatives, write an equation representing the growth of the population. Let k be the constant of proportionality.

(b) Show that the function P(t) = Ae^kt satisfies the equation in part (a) for any constant A.

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Physics: Using derivatives write an equation representing the growth

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