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Applied Calculus (MAT 121) Dr. Day Thur sday March 8, 2012

Applied Calculus (MAT 121) Dr. Day Thur sday March 8, 2012. Continuously Compounded Interest (5.3) Continuous Compounding compared to Periodic Compounding Solving Problems: What’s the Unknown?. Exponential Functions. Big Ideas What are Exponential Growth and Exponential Decay?

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Applied Calculus (MAT 121) Dr. Day Thur sday March 8, 2012

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  1. Applied Calculus (MAT 121)Dr. DayThursday March 8, 2012 • Continuously Compounded Interest (5.3) • Continuous Compounding compared to Periodic Compounding • Solving Problems: What’s the Unknown? 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. Compound Interest Suppose $2500 is deposited in a savings account earning 1.25% annual interest compounded annually. Assuming no deposits or withdrawals, what will be the value of the account in 8 years? What if the same the account used continuously compounded interest? MAT 121

  6. Compound Interest Assume continuous compounding for the following problems. • Calculate the amount accumulated after 3 years if $7800 is invested at 9% per year. How much of that is interest? • Calculate the interest rate needed for an investment of $8,000 to grow to $10,000 in 10 years. Round to the nearest hundredth of a percentage point. • How long will it take for an investment of $7,000 to double if the investment earns interest at the rate of 3% per year? • Calculate the principal required in order to create an account with a value of $25000 after 3 years at an interest rate of 12% per year. MAT 121

  7. Assignments WebAssign 5.3 due tomorrow 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. MAT 121

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