1. 8.1 Exponential Growth p. 465

2. Exponential Function f(x) = b x where the base b is a positive number other than one. Graph f(x) = 2 x Note the end behavior x→∞ f(x)→∞ x→-∞ f(x)→0 y=0 is an asymptote

3. Asymptote A line that a graph approaches as you move away from the origin The graph gets closer and closer to the line y = 0 ……. But NEVER reaches it y = 0 2 raised to any power Will NEVER be zero!!

4. Lets look at the activity on p. 465 This shows of y= a * 2 x Passes thru the point (0,a) (the y intercept is a) The x-axis is the asymptote of the graph D is all reals (the Domain) R is y>0 if a>0 and y<0 if a<0 (the Range)

5. These are true of: y = ab x If a>0 & b>1 ……… The function is an Exponential Growth Function

6. Example 1 Graph y = ½ 3 x Plot (0, ½) and (1, 3/2) Then, from left to right, draw a curve that begins just above the x-axsi, passes thru the 2 points, and moves up to the right

7. y = 0 Always mark asymptote!! D+ D= all reals R= all reals>0

8. Example 2 Graph y = - (3/2) x Plot (0, -1) and (1, -3/2) Connect with a curve Mark asymptote D=?? All reals R=??? All reals < 0 y = 0

9. To graph a general Exponential Function: y = a b x-h + k Sketch y = a b x h= ??? k= ??? Move your 2 points h units left or right …and k units up or down Then sketch the graph with the 2 new points.

10. Example 3 Graph y = 3·2 x-1 -4 Lightly sketch y=3·2 x Passes thru (0,3) & (1,6) h=1, k=-4 Move your 2 points to the right 1 and down 4 AND your asymptote k units (4 units down in this case)

11. y = -4 D= all reals R= all reals >-4

12. Now…you try one! Graph y= 2·3 x-2 +1 State the Domain and Range! D= all reals R= all reals >1 y=1

13. Compound Interest A=P(1+r/n) nt P - Initial principal r – annual rate expressed as a decimal n – compounded n times a year t – number of years A – amount in account after t years

14. Compound interest example You deposit $1000 in an account that pays 8% annual interest. Find the balance after I year if the interest is compounded with the given frequency. a) annually b) quarterlyc) daily A=1000(1+.08/1) 1x1 = 1000(1.08) 1 ≈ $1080 A=1000(1+.08/4) 4x1 =1000(1.02) 4 ≈ $1082.43 A=1000(1+.08/365) 365x1 ≈1000(1.000219) 365 ≈ $1083.28

15. Assignment