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6.2 Exponential Functions Notes

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This comprehensive guide delves into the fundamentals of exponential functions, distinguishing them from linear and quadratic equations. We'll explore the characteristics of exponential growth and decay, including their graphical representations based on their base and exponent values. Learn how to calculate compound interest and the impact of different compounding frequencies (annually, semiannually, quarterly, monthly, and daily) on investments. A step-by-step example illustrates calculating the final amount of an investment at 5% interest over ten years, using various compounding periods.

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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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