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Lesson 15-filled

# Lesson 15-filled - Math 1314 Lesson 15 Exponential...

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Math 1314 Lesson 15 Exponential Functions as Mathematical Models In this lesson, we will look at a few applications involving exponential functions. We’ll first consider some word problems having to do with money. Next, we’ll consider exponential growth and decay problems. Interest Problems From previous course work, you may have encountered the compound interest formula: mt m r P A + = 1 P = principal amount invested A = accumulated amount r = interest rate m = number of times interest is compounded per year t = time in years Now suppose we let the number of compounding periods increase; that is, we’ll take the limit of this function as m goes to infinity: mt m m r P + 1 lim This is a fairly complicated limit to evaluate, so we will omit the details. rt mt m Pe m r P = + 1 lim You may also have seen this formula before. This is the interest formula to use when interest is compounded continuously.

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