Differentlal Equatlons – Growth and Decay This lesson teaches how to use exponential functions to model growth and decay in applied problems. Consider the statement, "The rate of change of some quantity y is directly proportional to y." dy = ky dt The Law of Exponentlal Change If y is a differentiable function of t such that y> 0 and "y changes at a rate proportional to the amount present" (that is, if dy/dt = ky ), and for some constant k, then y = Ce*t Where C is the initial value of y, and k is the constant of proportionality. • When k >0 Exponential growth occurs, and • When k <0 Exponential decay occurs. EX #1: Prove that 2 = ky supports the model y Cet %3D

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.