2. 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

3. XY-22/92/3 02 16 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

4. XY-212525 05 11 · 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

5. 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:

6. 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

7.  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 ≈ $393.93 in 4 years

8. Complete a t-chart Domain: Range: Y-intercept: XY -23/4 3/2 03 16 212 (-∞,∞) (0,∞) (0,3)

9. Complete a t-chart Domain: Range: H. Asymptote: XY -29 5 03 12 21.5 (-∞,∞) (1,∞) Y=1

10. Equation:

11. X=7

12.  1. 2. 3 x = 27 3. 3 2X-1 =27 X+2

13. 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

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

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

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

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

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

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

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

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

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