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7.1 Do Now

7.1 Do Now. Use a table of values to graph . Graphing Exponential Growth Functions with Shifts. 1) Identify the parent. It is y=a* b^x . 2) Make a table of values for the parent using x=-1, 0, and 1. Graph.

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7.1 Do Now

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  1. 7.1 Do Now • Use a table of values to graph

  2. Graphing Exponential Growth Functions with Shifts • 1) Identify the parent. It is y=a*b^x. • 2) Make a table of values for the parent using x=-1, 0, and 1. Graph. • 3) Identify the shifts left/right (this will be “in the exponent”, recall that + is left) and up/down (this will be “at the end”). Use the shift to obtain the translated function. • 4) Identify the asymptote. y=k (the vertical shift) • 5) The domain is all real numbers. The range is found from the graph using the asymptote.

  3. Example

  4. You Try!

  5. Ewww…Fractions

  6. Word Problems Starring Exponential Growth

  7. You Try!

  8. 7.2Do Now: HW Out for a Check and: • Use a table of values to graph

  9. Same Game as Yesterday…Almost

  10. Follow the Same Steps We Covered Yesterday!

  11. Another

  12. Decay Word Problems

  13. You Try!

  14. Do Now • Are each of these exponential growth, exponential decay, or neither?

  15. The amount g (in trillions of cubic feet) of natural gas consumed in the United States from 1940 to 1970 can be modeled by g = 2.91(1.07)t , where t is the number of years since 1940. a. Identify the initial amount, the growth factor, and the annual percent increase. b. Estimate the natural gas consumption in 1955.

  16. The number A (in millions) of record albums sold each year in the United States from 1982 to 1993 can be modeled by A = 265(0.39)t, where t represents the number of years since 1982. a. Identify the initial amount, the decay factor, and the annual percent decrease. b. Use the graph to estimate when the number of records sold was 1 million.

  17. You buy a new car for $30,000. The value of the car decreases by 15.7% each year. a. Write an exponential decay model for the value of the car. Use the model to estimate the value after 3 years. b. Estimate when the car will have a value of $800.

  18. Exploring “e” Start by making sure your window is the standard one Enter (1+1/x)^x as Y1 in your calculator Go to Tblset-Choose tblstart=1 and increments of 5 Go to Table-as the x values get bigger, what seems to be happening to the y values? Confirm what is happening with the graph

  19. e • Euler’s number • Used for continuously compounding interest • Used for probability density functions • Population models Etc. REMEMBER-e is a number, not a variable!

  20. Use Your Calculator to Evaluate to Nearest Hundredth

  21. Simplify without a Calculator

  22. 7.3 Do Now

  23. Graphing Exponential Growth and Decay, With “e” Today…MESSY NUMBERS

  24. Remember • e is a number—just graph these suckers like you did the exponential growth and decay of last week!

  25. Example

  26. Another!

  27. You Try!

  28. Exponential Growth, Decay, or Neither?

  29. Application

  30. Do Now- Interest

  31. Interest

  32. Example

  33. For Continuously Compounded Interest

  34. 7.4 Do Now • Solve for x.

  35. What are logarithms? log·a·rithm : noun the exponent that indicates the power to which a base number is raised to produce a given number Merriam-Webster Online (June 2, 2009)

  36. What are logarithms used for? • pH Scale • Richter Scale • Decibels • Radioactive Decay • Population Growth • Interest Rates • Telecommunication • Electronics • Optics • Astronomy • Computer Science • Acoustics … And Many More!

  37. The logarithmic function is an inverse of the exponential function.

  38. Logarithm with base b The basic mathematical definition of logarithms with base b is… logb x = y iff by = x b > 0, b ≠ 1, x > 0

  39. Write each equation in exponential form. • log6 36 = 2 2. log125 5 = 1 5

  40. Write each equation in logarithmic form. • 3. 23 = 8 • 7-2 = 1 • 49

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