a≠0, b>0,b≠1, xєR Exponential Growth Exponential Decay (0,a) b > 1, b = ___ a = H. Asymptote: y = 0 < b < 1, b =

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a≠0, b>0,b≠1, xєR Exponential Growth Exponential Decay (0,a) b > 1, b = _______________ a = __________________ H. Asymptote: y = ______ 0 < b < 1, b = _______________ a = _________________ H. Asymptote : y = ______ growth factordecay factor y-intercept on parent fcn 00 NOTES DAY 8.1

XY-22/92/ The “b” is NOT the y-intercept in an exponential function · 3· 3 · 3· 3 · 3· 3 +1 “a” is the starting point and b is the product from one y-value to the next Y = 2 · 3 x

XY · 1/5· 1/5 · 1/5· 1/5 · 1 / 5 +1 The “a” is the starting point and so a = 5 y = 5 · ( 1 / 5 ) x The b is the product, so b = 1 / 5 Where a≠0 0<b<1

Causes a _________________ in the graph Causes a _____________ in the x-axis “h” causes a _______________________ in the graph “k” causes a _______________________ in the graph Vertical Translation Vertical Shrink Reflection Horizontal Translation Vertical Stretch Parent: Transformation:

Y = a(1+r) t a = initial amount r = growth rate t = time period 1+r = growth factor If the rate is 3%, then The decay model is the same except the decay factor is 1 – r 1.03 is the growth factor

 You put $350 in a savings account that earns 3% annual interest compounded yearly. How much will that investment be worth in 4 years? Y = a(1+r) t Y = 350(1+0.03) 4 Y ≈ $ in 4 years

Complete a t-chart Domain: Range: Y-intercept: XY -23/4 3/ (-∞,∞) (0,∞) (0,3)

Complete a t-chart Domain: Range: H. Asymptote: XY (-∞,∞) (1,∞) Y=1

Equation:

X=7

 x = X-1 =27 X+2

Activity: Now lets see what you know. I will show you some problems. When I ask for the answer, please show the color of the matching correct answer. HW : WS 8.1

 A. x = 0  B. y = 0  C. x = 2  D. y = 2

 A. Y = 3 x  B. Y = 3 x  C. Y = 3 x  D. y = 3 x-3 +1

 A. Y = 3 x  B. Y = 3 x  C. Y = 3 x  D. y = 3 x-3 + 1

A. Translated up 1 unit B. Translated down 1 unit C. Reflected over the x-axis D. Reflected over the y-axis

A. y=2(3) x B. y=3(2) x C. Y=2x 3 D. y=3x 2

A. y=50(3) 5 B. y=50(1.03) 5 C. Y=3(50) 5 D. y=1.03(50) 5

 A. 2x+2=81/3  B. 3 2x+2 =3 4  C. 9 x+2 = 81  D. 3 2x+2 = 9 2

 A. X = X-4  B. 3 x =3 -2X+8  C. 3 x = (3 2 ) X-4  D. X = 2X-4

 A. X-5 = 1  B. 4 x-5 = 4 3  C. 4 x-5 =  D. X-5 = 64