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Lecture 4.2 bt


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Lecture 4.2 bt

  1. 1. Today’s Agenda  Attendance / Announcements  Sections 4.1b / 4.2  Quiz Friday
  2. 2. More Exponential Applications Banking – Compounded Interest Situation: An amount (“Principal”) is deposited into an account. An interest rate (usually growth) is applied to the amount in the bank at specific times throughout the year. The amount in the bank at any time can be found using….
  3. 3. Amount of money in bank (balance) t, Number of years money left in account r, Interest rate (as a decimal!) r A P1 n nt P, amount initially n, Number of times deposited, principal compounded PER YEAR
  4. 4. Find the amount when $9000 is invested at 5.4% compounded monthly for 6 years.
  5. 5. A total of $12,000 is invested at an interest rate of 3%. Find the balance after 4 years if the interest is compounded quarterly.
  6. 6. Example: You deposit $5,000 into an account with a 6.5% interest rate. Find the amount in the account after 10 years.
  7. 7. What happens if interest is compounded more than daily, hourly, every minute!? Continuously! r A P1 n nt rt A Pe What is e ?
  8. 8. 1 e lim 1 x x x So, it’s just a constant number between 2 and 3! 2.718
  9. 9. Find the amount when $5400 is invested at 6.25% compounded continuously for 6 months rt A Pe
  10. 10. Finding Exponential Functions Need initial value (0, …), and another data point (x, y). Substitute into exponential function: f ( x) a b x Solve for the growth/decay rate. Then rewrite exp. function. (similar to what we’ve done before)
  11. 11. Finding Exponential Functions Find the exponential function of the form that passes through the points (0,100) and (4, 1600) f ( x) a b x
  12. 12. Finding Exponential Functions A population of bacteria grew from 24 to 615 over the course of 5 hours, find an exponential function to model this growth f ( x) a b x
  13. 13. Finding Exponential Functions The table shows consumer credit (billions) for various years. Find an exponential function and estimate credit for the year 2016 f ( x) a b x
  14. 14. Classwork • Worksheet