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# Mth141s56 - Sec 5.6 Applications and Models Growth and...

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Sec. 5.6 – Applications and Models : Growth and Decay We mentioned that the base e is used frequently in exponential, and therefore logarithmic, equations involving science and business. Earlier we saw how interest can be calculated by compounding. There are actually two formulas used to calculate money that has the interest compounded. Periodic compounding (1 ) nt r A P n = + Continuous compounding rt A Pe = Ex. Keith has discovered thru a rather tedious process that he is losing 3% of his hair each year. After 5 years, how much of his hair will still remain? Since this is a continuous compounding example, we use rt A Pe = .03(3) 100 A e - = .09 .09 100 100 A e A e - - = = 100(.9139311853) A = A = 91.4% Ex. Farmer Sue decides to sell off 2% of her land each year to pay the property taxes. After 4 years, what percent of her original land will she still have? This is an example of periodic compounding, so : (1 ) nt r A P n = + 1(4) .02 100(1 ) 1 A - = + 4 100(.98) A = 100(.92236816) A = A = 92.2%

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Our book mentions the basic exponential growth function used in the sciences : 0 ( ) kt A t A e = where A 0
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