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Exponential growth and decay modeled by continuous dynamical systems

 

Video

Exponential growth and decay in continuous dynamical systems.

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Question

For the differential equation \begin{align*} \diff{x}{t} &= rx\\ x(0) &= x_0, \end{align*} what is the condition for the solution to exhibit exponential growth?

What is the condition for the solution to exhibit exponential decay?

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Elementary dynamical systems
Math 1241, Fall 2020
Math 201, Spring 22