1. Stamp Investigation 1. What is exponential growth? 2. Where do we commonly see exponential growth in the world around us? 3. How was the previous investigation (Checkers Investigation) an example of exponential growth? 4. Are exponential equations linear?

2. Looking Back The Checkers Investigation -Was your graph linear? -Were you able to find a slope? -Were your numbers increasing or decreasing? -What happened when the numbers got too big for the calculator? -What does E mean on the calculator?

3. Brainstorm What in your life or the lives of those around you do you think may increase exponentially? (Hint increases very fast) Rabbit Population

4. The Background Story When Sam was in 7 th grade, his aunt gave him a 20 stamp collection worth $2500. Sam considered selling the collection, but his aunt told him that, if he saved it, it would increase in value. Sam saved the collection, and its value increased by 6% each year for several years in a row.

5. Objectives Use action words! Analyze Classify Identify Describe Apply Explain Convert Compare/Contrast Assess Conclude Relate Interpret

6. Objectives 1.Evaluate data that shows exponential growth 2.Interpret parabolic relationships 3.Express parabolic data in a table, graph, and an equation

7. Hypothesis I believe… 1.Think about what we are trying to find through our data 1.Think about if the data will grow or decay

8. Hypothesis I believe Sam’s collection will be worth ___________ after 20 years. I believe there will/ won’t be a (Linear/ Parabolic/ Hyperbolic) pattern to this data. I believe that this data will (grow/decay).

9. Materials What will we use to do this investigation?

10. Materials 1.Stamp Sheet 2.Paper 3.Calculator 4.Pencil 5.Markers/ Crayons/ Colored Pencils

11. Procedure What steps will we take to do this investigation? Remember even the small steps! -Checkers Investigation – cutting off the rectangle

12. Procedure 1.Create a data table for years 1-20 2.Look at the stamp sheet and calculate the worth of each stamp. 3.Calculate the worth of the stamp collection for years 1-20. 4.Create a graph based on your data. 5.Develop an equation for the data set.

13. Data Create a data table to use during the investigation How many years should be on the data table? What will X represent? What will Y represent?

14. Observations Remember to make 3 observations as you are doing the investigation!

15. Calculations Can we find a slope for this data? Can we find an equation for this data? What will the graph look like for this data? -Pancake? -Uptown/Downtown? -2 C’s Make a table of only the first 5 years of this data What is the growth rate for this data?

16. Conclusions 1. Respond to your hypothesis. 2. What are some potential errors that may have effected this investigation? How?

17. Conclusions 1.Growth or Decay? 2.Linear? Parabolic? Hyperbolic? 3.Errors and Effects? 4.What is one stamp worth after 20 years? 5.What is the whole collection worth after 20 years?

18. Extension Problems 1. Suppose the growth rate changed to 4%. Make a table, equation, and graph for years 1-10. 2. Convert the following growth rates to growth factors: 5%, 15%, 30%, 75%, 100%, 150%. 3. Convert the following growth factors to growth rates: 1.5, 1.25, 1.1.