1. Review of Quadratics and Exponentials

2. QUADRATICS Analyzing Data, Making Predictions Quadratic Functions and Graphs – Graph is a curve, opened up or down – Y=ax²+bx+c – Data TREND is a more dramatic increase or decrease – Examples from class - Chicago Water Arc - Path of a baseball and bullet - Average monthly temperatures in Buffalo - Roller Coasters - Tire Marks and braking distance

3. Quadratic Example The school drinking fountain can be modeled using the equation: y= -0.3988x²+2.1785x+1.63 The drinking fountain spout is 1 5/8” above the bowl. Type the equation in y=. Turn plots off. Set WINDOW. What is the greatest height the water reaches? How far across the bowl does the water reach?

4. Graph of Drinking Fountain

5. Exponentials Analyzing Data, Making Predictions Exponential Functions and Graphs – Graph is a steep curve, opened up or down – y=a*b^x - Data TREND is dramatic increase or decrease Examples from class - Mythbusters and paper folding - Power of the Penny - World Population Growth - Drug Dosage - Compound Interest - Speed versus time - Bacteria Growth

6. Exponential Example THE RISE OF STARBUCKS You are going to develop a model for the growth in the number of Starbucks Coffee stores since it was founded in 1971. The table below indicates the progression of store openings since the company was founded in 1971. YearYears since Starbucks opened LIST 1 (x) Number of stores LIST 2 (y) 197101 1984136 19871617 19891855 199322272 199524676 1997261412 1999282500 2003327000 20053410500 20063512440 20073615011 20083716680 20103916858 20124117651

7. Graph of Starbucks Expansion Make two LISTS. L1 is the Years since Starbucks opened and L2 is the corresponding number of stores. STAT PLOT ON. WINDOW. GRAPH. Label and sketch the graph on the next page. What function appears to be the best model? What does the graph look like? Find the regression equation that best fits the growth of Starbuck stores. STAT. CALC. #0, ExpReg, ENTER. Y=______________________ Using your regression equation from question #3, approximate the number of stores at the close of 2015. (if x=44, then y=?) _________________

8. Starbucks Growth Graph Do you think Starbucks’ management is pleased with the growth of their brand? List one reason for the tremendous growth of Starbucks since inception. List one reason for a possible decline in the growth of Starbucks in the near future. Label and sketch the growth of Starbucks from 1971 to the present on the graph to the left.