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

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Presentation on theme: "2/27/2016 exponential growth and exponential decay larry scandone Gavin Middle School."— Presentation transcript:

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

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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

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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.

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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


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