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Differential Equations for Exponential Growth and Decay

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Explanations 2

The exponential growth and decay formulas can be seen two different ways: as formulas, which they are called on a day-to-day basis; as differential equations, the other way to l…
By Katherine Rosinski, Alex Federspiel
We revisit exponential growth and decay from the perspective of differential equations: namely, the exponential differential equation, y′=kyy' = kyy′=ky, where kkk is a constant…
By Victor Wang

Problems 1

Let fff be a real smooth (i.e. infinitely-differentiable) function such that f′(x)2=f(x)f′′(x)f'(x)^2 = f(x) f''(x)f′(x)2=f(x)f′′(x) for all real xxx. Suppose f(0)=1f(0) = 1f(0)…