1. DO NOW: YOUR PARENTS HAVE DECIDED TO CHANGE YOUR ALLOWANCE AND YOU MUST DECIDE WHICH PLAN WILL GIVE YOU MORE MONEY NEXT MONTH. PLAN A – ON THE FIRST DAY YOU WILL RECEIVE 1 CENT, THE SECOND DAY 2 CENTS, THE THIRD DAY 4 CENTS…..AND SO ON…EACH DAY THE AMOUNT OF MONEY YOU RECEIVE WILL DOUBLE. PLAN B – YOU WILL RECEIVE $100 EACH DAY.

2. Objective: By then end of class today, I will be able to graph exponential functions. PLAN A – IS AN EXAMPLE OF AN EXPONENTIAL FUNCTION

4. Exponential Functions An exponential function is a function of the form: where x is always the exponent

5. EXPONTENTIAL FUNCTIONS Compound interest Some populations increase at a rate of 2 % each year. Radioactive half-life Bacteria growing Vehicles or something loses value at a rate of 11% per year

6. First, let’s take a look at an exponential function xy = 2 x y 02020 1 12121 2 22 4 2 – 1 1/2 -22 – 2 1/4

7. What is the y-intercept of this graph? Answer: The y -intercept is 1. 93232 2 33131 1 13030 0 3 –1 –1 y3x3x x Graph y = 3 x from –1 ≤ x ≤ 2

8. Answer: The y -intercept is 1. Graph y = 5 x from –2 ≤ x ≤ 2 and find the y-intercept xy = 5 x y -25 – 2 1/25 5 – 1 1/5 05050 1 15151 5 25252 25

9. LET’S GRAPH THE FOLLOWING: y = 4 X y = 15 X Then make 4 conclusions about your graphs. Y-intercept always = 1 Graph is above the x – axis The greater b, the steeper the graph The graph will never touch the x-axis

11. Next, observe what happens when b assumes a value such that 0<b<1. Graph each in your calculator and sketch: What is different about these graphs? What is similar?

12. This is what your graphs should look like.

13. Now on the same graph – graph the following What do you notice?

14. Our general exponential form is “b” is the base of the function and changes here will result in: When b>1, the graph increases. When 0<b<1, the graph decreases.