sn1_1 - Math 1432 Notes Session 1 7.6 Exponential Growth...

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Math 1432 Notes – Session 1 7.6 Exponential Growth and Decay Many quantities change with a rate proportional to time: ky dt dy = Solving: Ex: Find a function that satisfies y y 2 = and 4 ) 0 ( = y
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You try! (hw6 #5) Solve for y : x x e e dx dy 2 2 1 - - + = a. C e y x + = - 2 sin 2 1 b. C e y x + - = - 2 arctan 2 c. C e y x + + - = - ) 1 ln( 2 1 2 d. C e x y x + + = - ) 1 ( 2 2 e. none of these
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Applications: Population Growth: kt e P t P ) 0 ( ) ( = Radioactive Decay: kt e A t A ) 0 ( ) ( = if T is the half-life then 2 ln - = kT Compound Interest: rt e A t A ) 0 ( ) ( = Examples 1. A certain species of virulent bacteria is being grown in a culture. It is observed that the rate of growth of the bacterial population is proportional to the number present. If there were 5000 bacteria in the initial population and the number doubled after the first 60 minutes, how many bacteria will be present after 4 hours? 2.
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This note was uploaded on 03/07/2012 for the course MATH 11278 taught by Professor Jeffmorgan during the Summer '10 term at University of Houston.

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sn1_1 - Math 1432 Notes Session 1 7.6 Exponential Growth...

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