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6.2 Exponential Functions Notes

6.2 Exponential Functions Notes. Linear, Quadratic, or Exponential? Exponential Growth or Decay? Match Graphs Calculate compound Interest. Linear, Quadratic, or Exponential?. Linear looks like: y = mx+b Quadratic looks like: y = ax 2 +bx+c Exponential looks like: y = a•b x.

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6.2 Exponential Functions Notes

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  1. 6.2 Exponential FunctionsNotes Linear, Quadratic, or Exponential? Exponential Growth or Decay? Match Graphs Calculate compound Interest

  2. Linear, Quadratic, or Exponential? • Linear looks like: • y = mx+b • Quadratic looks like: • y = ax2+bx+c • Exponential looks like: y = a•bx exponent y = a•bx coefficient base

  3. Examples: • f(x) = (77 – x)x • g(x) = 0.5x – 3.5 • h(x) = 0.5x2 + 7.5

  4. Growth or Decay? • Growth if: • base>1 and • exponent is positive • Decay if: • base<1 or • exponent is negative • Growth if (unusual case): • base<1 and exponent is negative

  5. Examples: • f(x) = 500(1.5)x • d(x) = 0.125(½)x • s(k) = 0.5(0.5)k • f(k) = 722-k

  6. Growth looks like: Base is smaller. Base is larger.

  7. Decay looks like: Base is smaller. Base is larger.

  8. Compound Interest • A = amount after t years • P = principal (original money) • r = interest rate • n = number of compounds per year • t = time in years

  9. Vocabulary • annually = 1 time per year • semiannually = 2 times per year • quarterly = 4 times per year • monthly = 12 times per year • daily = 365 times per year

  10. Example • Find the final amount of a $100 investment after 10 years at 5% interest compounded annually, quarterly, and daily. • P = 100, t = 10, r = .05, n = 1, 4, 365 (3 calcs)

  11. Example, part 2 • Find the final amount of a $100 investment after 10 years at 5% interest compounded annually, quarterly, and daily. • P = 100, t = 10, r = .05, n = 1, 4, 365 (3 calcs)

  12. Example, part 3 • Find the final amount of a $100 investment after 10 years at 5% interest compounded annually, quarterly, and daily. • P = 100, t = 10, r = .05, n = 1, 4, 365 (3 calcs)

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