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# Week 4 Notes Math 182

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This 2 page Class Notes was uploaded by Bethany Lawler on Friday September 18, 2015. The Class Notes belongs to Math 182 at Washington State University taught by S. Lapin in Summer 2015. Since its upload, it has received 37 views. For similar materials see Honors Calculus II in Math at Washington State University.

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Date Created: 09/18/15

Math 182 Notes Week 4 9 14 9 18 Exponential Models Growth Decay The formula for exponential growth is yt 3106 C is a constant k is the growth rate coefficient and yo is the original amount or population y t gives the growth rate and is equal to k yt tt is the relative growth rate The relative growth rate is a constant and therefore not time dependent Y0 Y0 To find the time it takes for the population or amount to double use the following formula 1n 2 T2 IE To find the projected population in t years the growth coefficient k and the original population yo need to be known k can be found if the population and a given time is known and the original population is known Similarly the original population can be found if k is known and the population at a specific time is given The formula for exponential decay is the same as for growth but k is negative yt 310639 Decay problems can be solved in the same way as growth problems The formula for the time it takes for half of the substance to decay halflife is 1n2 k T NIH Hyperbolic functions Identities ex e39x o s1nhx 2 exe39x o coshx 2 exe x o tanhx o cschx exex 2 o sechx exei exe39 o cothx exex cosh2 x Sinh2 x 1 1 tcmh2 x sech2 x Derivative identities o sinh x coshx o cosh x sinhx o tanh x sech2 x o csch x cschx cothx o sech x sechx tanhx o coth x csc2 x Solving problems 0 Hyperbolic function problems can be solved in the same way as other functions using identities and the definition of each function Integration Techniques U substitution 0 For composite functions the inner function can be replaced With the variable u o Chance the integration by setting du x dX 0 Change the limits by plugging them into fx Subtle substitution 0 Multiply fractions by another fraction equivalent to one ex E to simplify the integration 0 Split fraction if necessary into two or more fractions 0 Solve each fraction as an individual integral Using trigonometric identities 0 Use trig identities to change the integrand into something easier to integrate

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