1. Exponential Functions

2. When do we use them? Exponential functions are best used for population, interest, growth/decay and other changes that involve a rapid increase or decrease in data values. Exponential functions: y = a(b x ) Logarithmic functions: y = a + b ln x Logistic growth functions:

3. Let’s experiment! Enter the data in the table into your calculators for L 1 and L 2 Plot the data on your calculator X, years since 1969 Y, federal minimum wage 11.60 62.10 113.10 163.35 213.80 264.25 315.25

4. Exponential Regression Use your calculator to find the exponential regression equation. How well does the correlation coefficient, r, indicate that the model fits the data? Use this equation to predict the minimum wage in 2009.

5. Logarithmic regression Use your calculator to find the logarithmic regression equation. How well does the correlation coefficient, r, indicate that the model fits the data? Use this equation to predict the minimum wage in 2009.

6. Power Regression Use your calculator to find the power regression equation. How well does the correlation coefficient, r, indicate that the model fits the data? Use this equation to predict the minimum wage in 2009.

7. Which is best? Based on the correlation coefficients, which model will give the best prediction for minimum wage in the future? Based on this model that you chose, by which year will the minimum wage be $7.25?

8. How did we do? The federal minimum wage in 2009 was $7.25. How well did our equation do at predicting the future? Is this a fair model to continue using for future predictions?