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Applied Calculus (MAT 121) Dr. Day Wednesday March 7, 2012

Applied Calculus (MAT 121) Dr. Day Wednesday March 7, 2012. Review: Exponent Properties (5.1) Logarithms (5.2) Converting exponent form to log form Graphs of log functions Using logs to solve equations. Exponential Functions. Big Ideas What are Exponential Growth and Exponential Decay?

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Applied Calculus (MAT 121) Dr. Day Wednesday March 7, 2012

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  1. Applied Calculus (MAT 121)Dr. Day Wednesday March 7, 2012 • Review: Exponent Properties (5.1) • Logarithms (5.2) • Converting exponent form to log form • Graphs of log functions • Using logs to solve equations 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. Graphs of Exponential Functions MAT 121

  4. Application of Exponential Functions • The concentration of a drug in an organ at any time t (in seconds) is given by C(t) shown here, where C(t) is measured in grams per cubic centimeter (g/cm3). • (a) What is the initial concentration of drug in the organ? • (b) What is the concentration of the drug in the organ after 7 sec? (Round your answer to three decimal places.) • (d) What will be the concentration of the drug in the long run?  Hint: Evaluate  limt→ C(t). MAT 121

  5. Conversion: Exponential Form to Log Form MAT 121

  6. Graphs of Log Functions MAT 121

  7. 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

  8. Assignments WebAssign 5.2 due tonight 5.3 due Friday 3/9 Quiz #5? 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. MAT 121

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