1. Exponential Functions 1. Exponents Review Remember, the following basic exponent rules:

2. Exponential Functions 2. Exponential Functions Non-Linear Exponential Functions are functions where the variable is the exponent. Switched from quadratic Examples: f(x) = 3 x P(r) = 2000(1.05) r f(x) = 4( ½ ) x

3. Exponential Functions 3. Graphing Exponential Functions Ex1 (I DO): f(x) = 3 x XY -23 (-2) = 1/(3 2 ) =.111 3 (-1) = 1/(3 1 ) =.333 03 (0) = 1 13 (1) = 3 23 (2) = 9 53 (5) = 243 Find these two first When x=0, y coord. is y-intercept Plot at least 5 points to get a good sense of the function. You may want to space your x values out to see growth 3 decimal places

4. Exponential Functions 3. Graphing Exponential Functions Ex1 (I DO): f(x) = 3 x XY -2.111.333 01 13 29 5243

5. Exponential Functions Called exponential function because it grows exponentially Output values start really small and get really big, really fast. 3. Graphing Exponential Functions

6. Exponential Functions 3. Graphing Exponential Functions Ex2 (WE DO): f(x) = 2 x XY -22 (-2) = 1/(2 2 ) =.250 2 (-1) = 1/(2 1 ) =.500 02 (0) = 1 12 (1) = 2 22 (2) = 4 52 (5) = 32 Find these two first When x=0, y coord. is y-intercept Plot at least 5 points to get a good sense of the function. You may want to space your x values out to see growth 3 decimal places

7. Exponential Functions 3. Graphing Exponential Functions Ex1 (WE DO): f(x) = 2 x XY -2.250.500 01 12 24 532

8. Exponential Functions 3. Graphing Exponential Functions Ex2 (WE DO): f(x) = 4(1/2) x XY -24(0.5) (-2) = 4/(0.5 2 ) = 16 4(0.5) (-1) = 4/(0.5 1 ) = 8 04(0.5) (0) = 4(1) = 4 14(0.5) (1) = 4(0.5) = 2 24(0.5) (2) = 4(0.25) = 1 54(0.5) (5) = 4(0.0313) = 0.125 Find these two first When x=0, y coord. is y-intercept

9. Exponential Functions 3. Graphing Exponential Functions Ex2 (WE DO): f(x) = 4(1/2) x XY -216 8 04 12 21 50.125

10. Exponential Functions 4. Linear vs. Exponential Growth LinearExponential XY 12 24 36 48 510 f(x) = 2x +2 XY 12 24 38 416 532 times 2 Constant Rate Add/Subtract the same value to increase output Constant Growth Rate Multiply by the same value to increase output (sometimes written as % change)

11. Exponential Functions 4. Linear vs. Exponential Growth LinearExponential Always stated in units (NOT percent) Increase/Decrease is because of adding or subtracting (NOT multiplying) Which rate of change is it: linear or exponential? Always stated in percent or multiplication factor (NOT units) Increase/Decrease is because of multiplying (NOT adding) a) The fish in the sea are decreasing by 10% every year b) Mr. Vasu’s bank account increases by $3,000 every month Exponential: 10% change Linear: $3,000 change

12. Exponential Functions 5. How to find the Constant Multiplication Factor To find the constant mult. factor f(x) = 3 x XY -2.111.333 01 13 29 5243 Constant Growth Rate = y 2 y 1 0.333 0.111 = 3 1 0.333 =3 9 3 =3 243 9 =27 Must be consecutive ordered pairs 3.00 = 300%

13. Exponential Functions f(x) = 4(1/2) x XY -216 8 04 12 21 50.125 Constant Growth Rate = y 2 y 1 8 16 = 0.5 4 8 =0.5 2 4 =0.5 0.50 = 50% To find the constant mult. factor 5. How to find the Constant Multiplication Factor

14. Exponential Functions 6. How to find the Y- Intercept How to find the y-intercept? f(x) = 3 x XY -2.111.333 01 13 29 5243 Remember: X=0 at the y-intercept (0,1) is the y-intercept f(x) = 4(1/2) x XY -216 8 04 12 21 50.125 (0,4) is the y-intercept