Rate of Change - Exponential Functions

Master rate of change with exponential functions! Practice calculations, graph interpretation & function writing.

NUMBER OF COFFEE SHOPS_year_ _number of stores_1987 171988 331989 551990 841991 1161992 1651993 2721994 4251995 6771996 10151997 1412 1. Find the average rate of change for each period of time. Show your reasoning. 1987 and 1990 2. 1987 and 1993 3. 1987 and 1997 4. Make some observations about the rates of change you calculated. What do these average rates tell us about how the company was growing during this time period? 5. Use the graph to support your answers to these questions. How well do the average rates of change describe the growth of the company in:the first 3 years?the first 6 years?the entire 10 years? 6. f(x) = 4(6x) + 5What is the y-intercept? 4 5 0 9 7. f(x) = 4(6x) + 5What is the asymptote? 4 5 0 9 8. Use the table to write the exponential function._x_ _y_ 0 3 1 15 2 75 3 375 y = 3(5)^x y = 5(3)^x y = 15(5)^x y = 5(15)^x 9. The graph models the amount of radioactive element present over the course of a 10-minute experiment.What is the y-intercept and what does it represent in context? 20; how fast it is decreasing 20; the starting amount of the element 10; the starting amount of the element 10; the amount when the experiment was over 10. What is the average rate of change of the amount of the element over the 10-minute experiment? -5.0 g -2.0 g -1.8 g -0.2 g