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8.1-2 – Exponential Functions. Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range.

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Presentation on theme: "8.1-2 – Exponential Functions. Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range."— Presentation transcript:

1 8.1-2 – Exponential Functions

2 Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range.

3 *Sketch of graph must have y-intercept & four other coordinate points. Use the “table” function on your TI- 83!

4 Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range. *Sketch of graph must have y-intercept & four other coordinate points. Use the “table” function on your TI- 83!

5 Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range. *Sketch of graph must have y-intercept & four other coordinate points. Use the “table” function on your TI- 83! xy -20.25 0.5 01 12 24

6 Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range. *Sketch of graph must have y-intercept & four other coordinate points. Use the “table” function on your TI- 83! xy -20.25 0.5 01 12 24

7 Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range. *Sketch of graph must have y-intercept & four other coordinate points. Use the “table” function on your TI- 83! xy -20.25 0.5 01 12 24

8 Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range. *Sketch of graph must have y-intercept & four other coordinate points. Use the “table” function on your TI- 83! xy -20.25 0.5 01 12 24

9 Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range. *Sketch of graph must have y-intercept & four other coordinate points. Use the “table” function on your TI- 83! xy -20.25 0.5 01 12 24

10 Ex. 2 Sketch the graph of y = (⅞) x. Then state the functions domain & range.

11 xy -21.3061 1.1429 01 10.875 20.76563

12 Exponential Growth – for any equation in the form y = a x, a > 1

13 Exponential Decay – for any equation in the form y = a x, a < 1

14 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay.

15 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x

16 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x growth

17 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x growth b. y = (0.5) x

18 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x growth b. y = (0.5) x decay

19 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x growth b. y = (0.5) x decay c. y = 0.3(5) x

20 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x growth b. y = (0.5) x decay c. y = 0.3(5) x

21 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x growth b. y = (0.5) x decay c. y = 0.3(5) x growth

22 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x growth b. y = (0.5) x decay c. y = 0.3(5) x growth d. y = 4 -x

23 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x growth b. y = (0.5) x decay c. y = 0.3(5) x growth d. y = 4 -x = 1 4 x

24 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x growth b. y = (0.5) x decay c. y = 0.3(5) x growth d. y = 4 -x = 1 = 1 x 4 x 4

25 Exponential Growth – for any equation in the form y = a x, a > 1 Exponential Decay – for any equation in the form y = a x, a < 1 Ex. 3 Determine whether each exponential function represents exponential growth or decay. a. y = 7 x growth b. y = (0.5) x decay c. y = 0.3(5) x growth d. y = 4 -x = 1 = 1 x decay 4 x 4

26 Ex. 4 Solve each equation. a. 3 x = 3 2

27 Ex. 4 Solve each equation. a. 3 x = 3 2

28 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2

29 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81

30 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81

31 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81

32 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 ?

33 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4

34 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4

35 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4

36 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64

37 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64

38 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64

39 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6

40 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6

41 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6

42 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1

43 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓

44 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1

45 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1 4 -x = 16 2x + 1

46 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1 4 -x = 16 2x + 1

47 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1 4 -x = 16 2x + 1 4 -x = (4 2 ) 2x + 1

48 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1 4 -x = 16 2x + 1 4 -x = (4 2 ) 2x + 1 4 -x = 4 2(2x + 1)

49 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1 4 -x = 16 2x + 1 4 -x = (4 2 ) 2x + 1 4 -x = 4 2(2x + 1) 4 -x = 4 4x + 2

50 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1 4 -x = 16 2x + 1 4 -x = (4 2 ) 2x + 1 4 -x = 4 2(2x + 1) 4 -x = 4 4x + 2

51 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1 4 -x = 16 2x + 1 4 -x = (4 2 ) 2x + 1 4 -x = 4 2(2x + 1) 4 -x = 4 4x + 2 -x = 4x + 2

52 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1 4 -x = 16 2x + 1 4 -x = (4 2 ) 2x + 1 4 -x = 4 2(2x + 1) 4 -x = 4 4x + 2 -x = 4x + 2 -5x = 2

53 Ex. 4 Solve each equation. a. 3 x = 3 2 x = 2 b. 3 x = 81 3 x = 3 4 x = 4 c. 2 3x + 5 = 64 2 3x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1 4 -x = 16 2x + 1 4 -x = (4 2 ) 2x + 1 4 -x = 4 2(2x + 1) 4 -x = 4 4x + 2 -x = 4x + 2 -5x = 2 x = -2/5

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