2. Exponential Decay

3. Write the sequence and determine the common ration or difference

4. What does an exponential function look like? Common Ratio Exponent and Independent Variable Just some number that’s not 0 Why not 0? Dependent Variable

5. Exponential decay Initial Value: the first term of the sequence Decay rate: the common ratio, always less than 1 Decay factor: 1-decay rate

6. What does Exponential Decay look like? Consider y = (½) x Table of Values: x (½) x y -2 ½ -2 4 ½ -1 2 0 ½0½0½0½01 1 ½1½1½1½1½ 2 ½2½2½2½2¼ 3 ½3½3½3½31/8 Graph: Cool Fact: All exponential decay functions look like this!

7. Exponential Growth vs Decay

8. Exponential Decay In the exponential function y = 4(.55) x, identify the: Initial value ____________ Decay rate _____________ Decay factor____________

9. Use the graph to determine the function Decay rate:____ Decay factor:___ Initial Value:___ Y=___________ InputOutput

10. How can you tell if an exponential function is growth or decay?

11. Examples Determine if the function represents exponential growth or decay. 1. 2. 3. Exponential Growth Exponential Decay Exponential Decay

12. Car problem! A car bought for $50,000 depreciates at 12% per year. What is its value after 11 years? Initial Value:______ Decay Rate:______ Decay Factor:____ Function:____ Value after 9 years:_____

13. The NCAA holds an annual basketball The NCAA holds an annual basketball tournament every March. The NCAA holds an annual basketball The top 64 teams in Division I are invited to play each spring. When a team loses, it is out of the tournament.

14. Investigation: Tournament Play Fill in the following chart and then graph the results on a piece of paper. Then be prepared to interpret what is happening in the graph. After round x Number of teams in tournament (y) 064 1 2 3 4 5 6

15. Questions What is the initial value? What is the decay rate for the NCAA tournament? Name the explicit function for the NCAA tournament. What is the y-intercept?

16. Term n for what?!Term(n) After round x Number of teams in tournament (y) 1064 2132 3216 438 544 652 761