I show how solving a separable differential equation allows us to derive the exponential growth and decay model y=Ce^(kt) from the differential equation dy/dt=ky. I then work through and example involving inverse variation, direct variation, finding the equation of exponential growth given two points the function passes through, and finally carbon 14 dating.
EXAMPLES at 6:46 10:43 18:38 25:22
When arriving at the Continuous Compound Growth and Decay formulas I am writing y instead of IyI because in the context of these application problems. It is not reasonable that C would be a negative initial amount of substance and thus y will never be negative.
I would like to send out a HUGE THANK YOU to my YouTube student Jigyasa Nigam that did the Closed Captioning of this lesson for me. Your support and help is greatly appreciated:D
Check out http://www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com
Tagged under: Differential Equation (Concepts/Theories),inverse variation,direct variation,exponential growth,exponential decay,separable differential,equation,equations, life,carbon 14,Calculus (Concepts/Theories),Mathematics Education (Website Category),tarrou,tarrou' chalk talk,profrobbob,free,math
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