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Lesson 5-3

Lesson 5-3. Exponential Functions. Exponential Functions:. Exponential Functions:. Any function in of the form of: f(x) = ab x where a>0, and b>0 and b≠1. Parent graphs for the general exponential functions are:. Parent graphs for the general exponential functions are:.

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Lesson 5-3

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  1. Lesson 5-3 Exponential Functions

  2. Exponential Functions:

  3. Exponential Functions: Any function in of the form of: f(x) = abx where a>0, and b>0 and b≠1.

  4. Parent graphs for the general exponential functions are:

  5. Parent graphs for the general exponential functions are:

  6. Parent graphs for the general exponential functions are: b > 1

  7. Parent graphs for the general exponential functions are:

  8. Parent graphs for the general exponential functions are: 0 < b < 1

  9. If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2).

  10. If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2). Use the general format: f(x) = abx

  11. If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2). Use the general format: f(x) = abx f(0) = 3  (0,3)  3 = ab0  3 = a

  12. If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2). Use the general format: f(x) = abx f(0) = 3  (0,3)  3 = ab0  3 = a

  13. If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2). Use the general format: f(x) = abx f(0) = 3  (0,3)  3 = ab0  3 = a f(2) = 12  (2,12)  12 = (3)b2  4 = b2  + 2 = b

  14. If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2). Use the general format: f(x) = abx f(0) = 3  (0,3)  3 = ab0  3 = a f(2) = 12  (2,12)  12 = (3)b2  4 = b2  + 2 = b (b must be positive so b = 2.)

  15. If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2). Use the general format: f(x) = abx Therefore, our function is f(x) = 3(2)x.

  16. If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2). Use the general format: f(x) = abx Therefore, our function is f(x) = 3(2)x. Thus, f(-2) = 3(2)-2.

  17. If f is an exponential function and f(0) = 3, f(2) = 12, find f(-2). Use the general format: f(x) = abx Therefore, our function is f(x) = 3(2)x. Thus, f(-2) = 3(2)-2.

  18. When exponential functions are used to represent exponential growth and decay, the variable t is used to represent time. Our functions can easily be written as:

  19. When exponential functions are used to represent exponential growth and decay, the variable t is used to represent time. Our functions can easily be written as: f(t) = abt

  20. When exponential functions are used to represent exponential growth and decay, the variable t is used to represent time. Our functions can easily be written as: f(t) = abt but we just worked with this as

  21. When exponential functions are used to represent exponential growth and decay, the variable t is used to represent time. Our functions can easily be written as: f(t) = abt but we just worked with this as A(t) = A0(1 + r)t

  22. When exponential functions are used to represent exponential growth and decay, the variable t is used to represent time. Our functions can easily be written as: so, we now adjust and get

  23. When exponential functions are used to represent exponential growth and decay, the variable t is used to represent time. Our functions can easily be written as: so, we now adjust and get A(t) =A0b(t/k)

  24. When exponential functions are used to represent exponential growth and decay, the variable t is used to represent time. Our functions can easily be written as: so, we now adjust and get A(t) =A0b(t/k) (k = time needed to multiply A0 by b)

  25. A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given.

  26. A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given. Since 12 years is the time needed to multiply A0 by 2, form (2) gives:

  27. A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given. Since 12 years is the time needed to multiply A0 by 2, form (2) gives: A(t) = A0(2t/12)

  28. A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given. Since 12 years is the time needed to multiply A0 by 2, form (2) gives: A(t) = A0(2t/12) To express A(t) in form (1), reason as follows.

  29. A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given. Since 12 years is the time needed to multiply A0 by 2, form (2) gives: A(t) = A0(2t/12) To express A(t) in form (1), reason as follows.

  30. A bank advertises that if you open a savings account, you can double your money in 12 years. Express A(t), the amount of money after t years, in each of the two forms previously given. Since 12 years is the time needed to multiply A0 by 2, form (2) gives: A(t) = A0(2t/12) To express A(t) in form (1), reason as follows.

  31. Rule of 72: If a quantity is growing at r% per year (or month) then the doubling time is approximately 72 / r years (or months).

  32. For example, if a quantity grows at a rate of 8% per year then the quantity will double in approximately (72 / 8) or 9 years. If a population is growing exponentially at arate of 2% per month then the population will double in about (72 / 2) or 36 months.

  33. A radioactive isotope has a half-lifeof 5 days. This means that half the substance will decay in 5 days. At what rate does the substance decay each day?

  34. A radioactive isotope has a half-lifeof 5 days. This means that half the substance will decay in 5 days. At what rate does the substance decay each day?

  35. A radioactive isotope has a half-lifeof 5 days. This means that half the substance will decay in 5 days. At what rate does the substance decay each day? So, the daily rate of decay is 13%.

  36. Assignment: Pgs. 183-184 C.E. 1-10 all, W.E. 1-11 odd

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