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# 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
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. A 100-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water leaks out in the first 5 minutes, find the amount of water left in the tank 15 minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present.

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3.
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sn1_1 - Math 1432 Notes Session 1 7.6 Exponential Growth...

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