Exp_Growth_Decay_notes

# Exp_Growth_Decay_notes - Calculus 12AP Three things to...

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Exponential Growth and Decay Class Notes Three things to Review: 1. Solving Differential 2. Rate of Change 3. Direct Variation Equations (grade 11) Solve: dy dx = x y Rate of change of V = ______ y varies directly as x (V = Volume) ______ Rate of change of A = ______ * k is called the (A = Area) ________________ Rate of change of P = ______ y varies inversely as x (P = Population) ______ Many real world situations involve a rate of change of y that is directly proportional to y e.g. ____________________ or ____________________ Example 1. Population Problem: The population of a little town of Scorpion Gulch is now 1 000 people. The population is presently growing at about 5% per year. Write a differential equation that expresses this fact. Solve it to find an equation that expresses population as a function of time. Law of Exponential Change If y changes at a rate proportional to the amount present dy dt = ky and y = y 0 , when t = 0, then, Where k > 0 represents growth and k < 0 represents

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## This note was uploaded on 02/04/2011 for the course MATH 116 taught by Professor John during the Spring '10 term at St. Michael.

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Exp_Growth_Decay_notes - Calculus 12AP Three things to...

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