2. 2/27/2016 exponential growth and exponential decay larry scandone Gavin Middle School

5. Goal and Objective  You will be able to recognize patterns of exponential growth and exponential decay from looking at graphs, tables, and equations.  You will understand how the growth factor, decay factor, and starting values affect the graph. 3

6. Today’s Problem 4.3 on page 50.  EXPLORING EXPONENTIAL EQUATIONS  Lets look at the problem 4

8. First we are going to graph each equation on our graphing calculators, then the sketch and label each equation’s graph in the box provided on your worksheet.

10. In Exponential Equation Y= a ( b ^x)  a = the starting value  b = the decay factor or growth factor  x is the exponent of b

11. What we are looking for?  How does b ( the growth or decay factor effect our graph)?  How does an exponential growth graph differ from an exponential decay graph? 5

12. First we have to set the window

13. Set your X-min to 0

14. Set your X-max to 5

15. Set your Y-min to 0

16. Set your Y-max to 20

17. Now lets graph 1.25 as a growth factor raised to the x-power How would you describe this graph as X increases?

18. Then graph the growth factor 1.5 raised to the X-power

19. Then graph 1.75 raised to the X-power

20. And finally we’ll graph 2 raised to the X-power

21. 2^x 1.75^x 1.5^x 1.25^x What happens to our graphs as the growth factor increases.Where would 5^x be located, how about 1.1^x?

22. Now lets graph some exponential decay functions, but first we have to reset our window

23. Push the window button and set your X-min to 0, X-max to 5, Your Y- min to 0 and your Y-max to 1

24. Lets start with a decay factor.25 raised to the X-power How would you describe this graph as X increases?

25. Now let’s graph decay factor.5 raised to the X-power

26. And finally graph decay factor.75 raised to the X-power.75^x.5^x.25^x What happens to the graphs as the decay factor increases?

27. Some important Questions  What similarities do you notice among the graphs?  What differences do you notice?  How could you predict the shape of the graph for the equation y = b^x when given a specific value of b?  How does a growth factor compare to a decay factor? 1