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Exponential Growth & Decay

Exponential Growth & Decay. Applications that Apply to Me!. Exponential Function. What do we know about exponents? What do we know about functions?. Exponential Functions. Always involves the equation: b x Example: 2 3 = 2 · 2 · 2 = 8. Group investigation: Y = 2 x. Create an x,y table.

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Exponential Growth & Decay

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  1. Exponential Growth & Decay Applications that Apply to Me!

  2. Exponential Function • What do we know about exponents? • What do we know about functions?

  3. Exponential Functions • Always involves the equation: bx • Example: • 23 = 2 · 2 · 2 = 8

  4. Group investigation:Y = 2x • Create an x,y table. • Use x values of -1, 0, 1, 2, 3, • Graph the table • What do you observe.

  5. The Table: Results

  6. The Graph of y = 2x

  7. Observations • What did you notice? • What is the pattern? • What would happen if x= -2 • What would happen if x = 5 • What real-life applications are there?

  8. Group: Money Doubling? • You have a $100.00 • Your money doubles each year. • How much do you have in 5 years? • Show work.

  9. Money Doubling Year 1: $100 · 2 = $200 Year 2: $200 · 2 = $400 Year 3: $400 · 2 = $800 Year 4: $800 · 2 = $1600 Year 5: $1600 · 2 = $3200

  10. Earning Interest on • You have $100.00. • Each year you earn 10% interest. • How much $ do you have in 5 years? • Show Work.

  11. Earning 10% results Year 1: $100 + 100·(.10) = $110 Year 2: $110 + 110·(.10) = $121 Year 3: $121 + 121·(.10) = $133.10 Year 4: $133.10 + 133.10·(.10) = $146.41 Year 5: $146.41 + 1461.41·(.10) = $161.05

  12. Growth Models: Investing The Equation is: A = P (1+ r)t P = Principal r = Annual Rate t = Number of years

  13. Using the Equation • $100.00 • 10% interest • 5 years • 100(1+ 100·(.10))5 = $161.05 • What could we figure out now?

  14. Comparing Investments • Choice 1 • $10,000 • 5.5% interest • 9 years • Choice 2 • $8,000 • 6.5% interest • 10 years

  15. Choice 1 $10,000, 5.5% interest for 9 years. Equation: $10,000 (1 + .055)9 Balance after 9 years: $16,190.94

  16. Choice 2 $8,000 in an account that pays 6.5% interest for 10 years. Equation: $8,000 (1 + .065)10 Balance after 10 years: $15,071.10

  17. Which Investment? • The first one yields more money. • Choice 1: $16,190.94 • Choice 2: $15,071.10

  18. Exponential Decay Instead of increasing, it is decreasing. Formula: y = a (1 – r)t a = initial amount r = percent decrease t = Number of years

  19. Real-life Examples • What is car depreciation? • Car Value = $20,000 • Depreciates 10% a year • Figure out the following values: • After 2 years • After 5 years • After 8 years • After 10 years

  20. Exponential Decay: Car Depreciation Assume the car was purchased for $20,000 Formula: y = a (1 – r)t a = initial amount r = percent decrease t = Number of years

  21. What Else? • What happens when the depreciation rate changes. • What happens to the values after 20 or 30 years out – does it make sense? • What are the pros and cons of buying new or used cars.

  22. Assignment • 2 Worksheets: • Exponential Growth: Investing Worksheet (available at ttp://www.uen.org/Lessonplan/preview.cgi?LPid=24626) • Exponential Decay: Car Depreciation

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