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Component 4 Accelerated Patterns of Predictable Change

Component 4 Accelerated Patterns of Predictable Change. 4. Patterns of Change. t. t. y = C(1-r). y = C(1+r). 4. Patterns of Change. The Rich get Richer…. It Takes Money to Make Money…. Year 1. 4. Patterns of Change. $90 5% annual interest. 4. Patterns of Change. 5%. .05.

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Component 4 Accelerated Patterns of Predictable Change

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  1. Component 4 Accelerated Patterns of Predictable Change

  2. 4 Patterns of Change t t y = C(1-r) y = C(1+r)

  3. 4 Patterns of Change The Rich get Richer… It Takes Money to Make Money…

  4. Year 1 4 Patterns of Change $90 5% annual interest

  5. 4 Patterns of Change 5% .05 $4.50 + $90.00= $94.50 (.05)($90.00) = $4.50 New Principal = $94.50

  6. Year 2 4 Patterns of Change New Principal = $94.50 Exponential Growth (.05)($94.50) = $4.725 New Principal = $99.225

  7. 4 Patterns of Change 45 years later…

  8. 4 Patterns of Change t y = C (1 + r) Write Cinderella’s new equation. current balance rate of interest years since initial investment initial investment Check your Work

  9. 4 Patterns of Change What is Cinderella’s balance in 45 years? Write Cinderella’s new equation. y = 90 (1 + .05)45 or y= 90(1.05) 45 Check your Work

  10. 4 Patterns of Change y = key to enter 90(1.05)t What is Cinderella’s balance in 45 years? push trace then right arrowto trace x to 45 x =45 y =808.6507 press enter to learn the value of ywhen x = 45 Her $90 grew to $808!

  11. 4 Patterns of Change xy 45 808.6507 Press the 2nd andTABLE buttons and scroll to the time you wish to see. Continue

  12. Exponential Growth Exponential Decay

  13. 4 Patterns of Change t y = C (1 - r) current enrollment 5% rate of decay When will the current enrollment fall to 600? 1200 was opening enrollment in 2000 How many years will it take?

  14. 4 Patterns of Change Enter 1200(.95)t into y=. How can you learn the value of t (or x) when y= 600? Continue

  15. 4 Patterns of Change then press 0 to graph and arrow over to get as close as you can to y=600 x=14 y=585.21 Continue

  16. 4 Patterns of Change What advice can you give school administrators? then scroll to y < 600 x=14 y=585.21

  17. Advice

  18. 4 Patterns of Change Enrollment is projected to drop below 600 students in 14 years past 2000, or 2014.

  19. Component 1 This concludes Component 4. Linear Algebra Rules of Algebra Using Technology Patterns of Change 1 2 3 4 Start Post-Assessment

  20. Post Assessment

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