At last something I understand! I mean that's probably only because it's similar to stuff I learned about in pre calculus, but none the less I see this a progress in my calculus confidence. This week we studied exponential growth and decay. I liked this because it was a topic It’s like a baby step from what I had learned last year. Previously the content surrounding exponential growth and decay utilized a the formula y=a(1+r)^x or y=a(1-r)^x and that was pretty much it. This time around derivatives were incorporated in the form of Separable Differential Equations and The Law of Exponential Change. Separable Differential Equations allow multiple variable equations to be isolated on either side and anti differentiated for each variable. To describe growth the differential equation that is used to describe growth is dy/dx=ky where k is either the growth constant or the decay constant depending on whether it is positive or negative. By breaking it down and separating the variables you can anti differentiate both sides into ln |y| =kt+c after exponating both sides you get |y|=e^kt+c. After the property of exponents is applied it becomes the law of exponential change, y=ysubscript0 e^kt.
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January 2018
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