1. Exponential Functions Graphing Functions

2. Geometric Sequence A geometric sequence has a common ratio. Are these geometric sequences?

3. Page 116 #29 x1234… Y3579… x1234… Y361224…

4. Page 116 #29 x1357… Y3… x1357… Y35813…

5. Page 117 #29 X2468… y3-5-9… X1257… Y1

6. Page 117 #29 X25811… y8121827… X2534 y2-7-4 X021 Y8400.321.6

7. Exponential Function Characteristics Exponential functions model Geometric sequences. In a growth graph the pattern shows that the y values increase slowly at first as x increases and then it grows rapidly as x gets larger. In a decay graph the pattern shows that the y values decreases slowly at first as x increases and then it decays rapidly as x gets larger.

8. Graphs Xy 01 13 29 327 481

9. Graphing xy 01 10.5 20.25 30.125 40.0625

10. Which is growing faster? xy 01 12 24 38 416 xy 01 15 225 3125 4625

11. Which graph is steeper? Do these graphs show growth or decay? What point do these graphs have in common(Focal Point)? As x gets smaller what happens to y?

12. Which is steeper? Do these graphs show growth or decay? What point do these graphs have in common(Focal Point)? As x gets very large what happens to y?

13. Conclusion about Growth and Decay functions In the function If b>1, the function will show growth. In the function If 0<b<1, the function will show decay

14. Conclusions about common points All functions of the form have a common point at (0,1)

15. Focus B Simplest exponential function

16. Writing exponential functions On Jan 1 Donnie borrowed a dollar from his brother, Mike, who charged him 5% interest compounded daily. The function describing the amount of money he owes,y, in terms of days,x,is

17. Table XY 01 11.05 21.10 31.16 41.22 …… 253.39  What is the common ratio?  What is the connection between the base of the equation and the interest rate.

18. Connecting the situation to the equation If Donnie had borrowed $100 instead of $1, what would the equation be? If Mike had charged him 7% interest on his $100 loan, what would the equation be?

19. Page 118 #30 like this Leo buys a minivan for $18 000. The vehicle depreciates by 15% each year. Set up a table of values to show the van’s value for the first four years. What is the common ratio? x01234 y 18 000

20. Writing an exponential function If Bradford bought a rare stamp for $800. It appreciates 5% per year. What exponential function represents the value,y, of the stamp after x years?