1. Section 7.1: Graph Exponential Growth Functions Chapter 7: Exponential and Logarithmic Functions

2. Exponential Function Format: y = ab x, where a ≠ 0 and b is a positive integer other than one If a > 0, and b > 1, then the function is an exponential growth function and b is the growth factor. If a > 0, and 0 < b < 1 (b is a fraction), then the function is an exponential decay function and b is the decay factor.

3. Parent Function for Exponential Growth f(x) = b x, where b >1 x-axis is a horizontal asymptote Asymptotes: a line that is approached, but seldom touched Domain: all real numbers Range: y > 0 Graph rises from left to right because of “growth”

4. To Graph y = b x 1) Write the original function 2) Make and use a table of values for y = b x 3) Apply shifts to table of values for y = ab x-h + k 4) Plot points 5) Sketch with a smooth curve

5. y = b x Table of values: X- values -20123 Y- values b -2 b -1 1b 1 b 2 b 3

6. Special Note! b -2 = 1/b 2 b -1 = 1/b b 0 = 1

7. EX. y = 2 x y = 2 x Simplify… X-20123 Y2 -2 2 -1 2 0 2 1 2 2 3 X-20123 Y1/41/21248

8. Plot the Points (and note the asymptote) Asymptote at x-axis! Do Not cross the x-axis!

9. Sketch the curve and label!

10. EX 2. y= 3 x-2 - 1 y= 3 x-2 – 1 Shifts: Asymptote: down 1… so y = -1 X: right 2… so add 2 Y : down 1… so subtract 1 X-20123 Y= 3 x 1/91/313927 X012345 Y-8/9-2/302826

11. Plots Points and asymptote!

12. Sketch Curve…

13. Uses: Compound Interest: A = P(1 + r/t) nt P = principal investment r = annual rate (as a decimal) t = number of years n = number of times compounded per year Exponential Growth Y = a(1 + r) t a = starting population r = percent increase (as a decimal) t = amount of time (could be in years, days, hours, etc.)

14. To solve exponential growth probvlems: Step 1) Choose the formula Step 2) Identify each part Step 3) Substitute into formula Step 4) Solve.

15. Your Turn: 482: A:3,5,7,9,15,18,54,56 B: 8,11,17,20,24,58,62 C: 12,14,21,22,23