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Applied Calculus (MAT 121) Dr. Day Friday March 9, 2012

Applied Calculus (MAT 121) Dr. Day Friday March 9, 2012. Derivatives of Exponential Functions( 5.4) Review Derivative Rules Rules for Exponential Functions Using and Applying the Derivative. Exponential Functions. Big Ideas What are Exponential Growth and Exponential Decay?

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Applied Calculus (MAT 121) Dr. Day Friday March 9, 2012

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  1. Applied Calculus (MAT 121)Dr. Day Friday March 9, 2012 Derivatives of Exponential Functions(5.4) • Review Derivative Rules • Rules for Exponential Functions • Using and Applying the Derivative MAT 121

  2. Exponential Functions Big Ideas • What are Exponential Growth and Exponential Decay? • What sort of applications use exponential functions as their mathematical models? • What algebra do we need to remember to work with exponential functions? • How do we undo exponentiation? We need the inverse function, called the logarithm function. • Where does calculus fit in to all of this? MAT 121

  3. Using Logarithms to Solve Equations • Halley's law states that the barometric pressure (in inches of mercury) at an altitude of x mi above sea level is modeled by the function p(x) = 29.92e-0.2x   (x≥ 0) If the barometric pressure as measured by a hot-air balloonist is 23.2 in. of mercury, what is the balloonist's altitude? Round your answer to two decimal places. MAT 121

  4. Compound Interest Periodic Compounding • A: amount in account • P: amount of original deposit (principal) • i: annual interest rate, expresses as a decimal value • n: number of compounding periods per year • t: number of years the principal remains in account Continuous Compounding • A: amount in account • P: amount of original deposit (principal) • r: annual interest rate, expresses as a decimal value • t: number of years the principal remains in account MAT 121

  5. Review: Derivative Rules • Power Rule • Product Rule • Quotient Rule • Chain Rule MAT 121

  6. Derivatives of Exponential Functions • For y = ex: • For y=kex: • For y=eu(x): MAT 121

  7. Derivatives of Exponential Functions y= ex y= 3ex y=e-2x y= 5x3 + e5x y= (1+e2x)/(e-3x-x) MAT 121

  8. Using These Derivatives • Determine all intervals where the function f(x) = x2e-x is increasing and where it is decreasing. • Find the absolute extrema of the function. h(x) = ex2 - 4 on [-2,2]. • The percentage of alcohol in a person's bloodstream thrs after drinking 8 fluid oz of whiskey is modeled by the equation. A(t) = 0.29te-0.3t, 0 ≤ t ≤ 12. How fast is the percentage of alcohol in a person's bloodstream changing after 1/2 hr? After 5 hr? Round your answers to four decimal places. MAT 121

  9. Assignments WebAssign 5.4 due Monday 3/19 Reminder: Check results for Test #3 Look at the multiple-choice correction sheet. Review the written comments I added to your test. Study the solution guide available on course website. Be Safe! Stay Sober! Hug Your Mama When You Get the Chance! MAT 121

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