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6.5 Growth and Decay and Pop. Growth

# 6.5 Growth and Decay and Pop. Growth - the time required...

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Exponential Growth and Decay & Population Growth Section 6.5

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Exponential Growth and Decay Model If y is a differentiable function of t such that y > 0 and y ‘ = ky, for some constant k , then y = Cekt. C is the initial value of y. k is the proportionality constant.
® Exponenital growth occurs when k > 0. ® Exponential decay occurs when k < 0.

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Newton’s Law of Cooling states that the rate of change in the temperature of an object is proportional to the difference between the object’s temperature and the temperature of the surrounding medium. .
( ) 1 ln s s s kt s dy k y T dt dy kdt y T y T kt C y Ce T = - = - - = + = +

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Half-Life The Half-life of a radioactive element is

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Unformatted text preview: the time required for half of the nuclei present to decay. Half-life = ln 2 k Compound Interest Formulas Let P = amt. of deposit, t = # of yrs ., A = balance after t yrs., r = annual interest rate, and n = # of compoundings per yr. 1. Compounding n times per yr.: 2. Compounding continuously: nt n r P A + = 1 rt A Pe = Logistic Growth Model M = maximum population 1 kt M P Ce-= + Joke Time What is an insect that’s not feeling well? secant (sick ant) Who was a famous person that was not very healthy? “I sick” Newton...
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6.5 Growth and Decay and Pop. Growth - the time required...

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