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

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8.1-2 – Exponential Functions

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!

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!

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

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

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

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

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

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

xy

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 = x + 5 = 2 6

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 = x + 5 = 2 6

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 = x + 5 = 2 6 3x + 5 = 6

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x + 1

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x x = 16 2x + 1

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x x = 16 2x + 1

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x x = 16 2x x = (4 2 ) 2x + 1

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x x = 16 2x x = (4 2 ) 2x x = 4 2(2x + 1)

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x x = 16 2x x = (4 2 ) 2x x = 4 2(2x + 1) 4 -x = 4 4x + 2

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x x = 16 2x x = (4 2 ) 2x x = 4 2(2x + 1) 4 -x = 4 4x + 2

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x x = 16 2x x = (4 2 ) 2x x = 4 2(2x + 1) 4 -x = 4 4x + 2 -x = 4x + 2

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x x = 16 2x x = (4 2 ) 2x x = 4 2(2x + 1) 4 -x = 4 4x + 2 -x = 4x x = 2

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 = x + 5 = 2 6 3x + 5 = 6 3x = 1 x = ⅓ d.(¼) x = 16 2x x = 16 2x x = (4 2 ) 2x x = 4 2(2x + 1) 4 -x = 4 4x + 2 -x = 4x x = 2 x = -2/5