5 4 the number e

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5 4 the number e

  1. 1. Objectives: 1. Define and apply natural base exponential functions.
  2. 2. Discovered by mathematician Leonhard Euler. (Sounds like “oiler”) Called the natural base e or the Euler number. Very common in higher math, especially calculus.
  3. 3. The irrational number e is defined: Means as n increases, gets closer and closer to e ≈ 2.718 n 10 100 1000 10,000 100,000 1,000,000
  4. 4. Compound interest can be measured using the equation: where P is principal, and n is the number of times interest is compounded per year.
  5. 5. If $1000 is invested at 8% annual interest, how much will you have after one year if interest is compounded: Quarterly? Daily?
  6. 6. As n gets very large the interest formula approaches . Example: How much will you have from the last example if interest is compounded continuously?
  7. 7. Compound/continuous interest yields annual growth that is greater than the annual interest rate indicates. The actual growth is described by the Effective Annual Yield. To find: Divide then write increase as a %.
  8. 8. After one year during which interest is compounded quarterly, an investment of $800 is worth $851. What is the effective annual yield?
  9. 9. What is the effective annual yield if you invest $200 and it is worth $297 after 1 year?
  10. 10. Any quantity, such as population, where compounding happens “all the time” can be expressed:
  11. 11. A population of ladybugs multiplies rapidly so the population after t days is How many ladybugs are present now? How many will there be after a week?

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