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Exponential Graphs

Exponential Graphs. Warm Up. Solve:. Find the Vertex:. Definition. In an exponential function, the base is fixed and the exponent is a variable. Exploration. Using your GDC, graph the following exponential functions on the same screen:. Exploration.

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Exponential Graphs

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  1. Exponential Graphs

  2. Warm Up Solve: Find the Vertex:

  3. Definition • In an exponential function, the base is fixed and the exponent is a variable.

  4. Exploration • Using your GDC, graph the following exponential functions on the same screen:

  5. Exploration • What do you observe about the function as the base gets larger, and the exponent remains positive?

  6. Exploration • Using your GDC, graph the following exponential functions on the same screen:

  7. Exploration… • Using your GDC, graph the following exponential functions on the same screen:

  8. Continued….

  9. Graph: HA: y = 0 Domain: Range:

  10. Graph: Decreasing! HA: y = 0 Domain: Range:

  11. Graph: HA: y = 0 Domain: Range:

  12. Graph: HA: y = 2 Domain: Range:

  13. Graph: HA: y = -3 Domain: Range:

  14. Graph: HA: y = -5 Domain: Range:

  15. Graph: HA: y = 2 Parent Function Right 4 Up 2 Domain: Range:

  16. Natural exponential function

  17. Graph: Left 1 Down 3 Domain: Range:

  18. Logarithmic Function • It’s the inverse of the exponential function Switch the x’s and the y’s!

  19. Graph: Is the inverse of Domain: Range: Domain: Range:

  20. Graph: Up 3 from previous example! Domain: Range:

  21. Graph: Left 4 from Original Example! Domain: Range:

  22. Graph: Right 2 from Original Example! Domain: Range:

  23. Graph: Reflected over y-axis. Domain: Range:

  24. Graph: Reflected over x-axis. Domain: Range:

  25. Compound Interest

  26. How many infected people are there initially? How many people are infected after five days? An infectious disease begins to spread in a small city of population 10,000. After t days, the number of persons who have succumbed to the virus is modeled by the function:

  27. Compound Interest P = Principal r = rate t = time in years n = number of times it’s compounded per year Compounded: annually n = 1 quarterly n = 4 monthly n = 12 daily n = 365

  28. Find the Final Amount: $8000 at 6.5% compounded quarterly for 8 years

  29. Find the Final Amount: $600 at 9% compounded daily for 20 years

  30. Find the Final Amount: $300 at 6% compounded annually for 25 years

  31. Compounded Continuously: P = Principal r = rate t = time in years E = 2.718281828…

  32. Find the Final Amount: $2500 at 4% compounded continuously for 25 years

  33. Suppose your are offered a job that lasts one month, and you are to be very well paid. Which of the following methods of payment is more profitable for you? How much will you make? • One million dollars at the end of the month. • Two cents on the first day of the month, 4 cents on the second day, 8 cents on the third day, and, in general, 2n cents on the nth day. More Profitable

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