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3.2 Finding Power Equations “x” cannot equal zero Remember, the format of a power equation is y ax Previously, when we had a table of data we could use different values to represent the years (like: let 1990 be year 0). For power equations to work, you can’t do this. The equation will “fail.” Instead, we take the first year and set it equal to a different number (like maybe 10). b Make sure you read your test to get more of an explanation here. Debt (thousands) 2010 $39.88 1. The American debt per capita is shown in the chart. This is the total 2011 $45.09 debt divided among every man, woman and child in America … 2012 $48.60 2013 $52.09 wow! 2014 $52.69 a) Consider 2009 to be year 0 and use regression to find a power equation to model the data. Round the numbers in your equation to 2 decimal places. b) Use your equation to predict the debt in 2016. Practice Year Solutions: a) Adding a column to the table will help with the data entry. Enter into the calculator the data from the table, then select the power option to generate the regression equation: 0.18 y 39.897 x Years Since 2009 Year Debt (thousands) 1 2 3 4 5 2010 2011 2012 2013 2014 $39.88 $45.09 $48.60 $52.09 $52.69 b) 2016 2009 7 Using the equation from a), substitute 7 for x and solve for y. y 39.897 70.18 y 56.631 y $56, 631 9. Practice Since we now have quadratic and power models that both accommodate curved data, reconsider the previous question. a) Notice the power curve in the previous question is not a great fit to the data (compare the fit of a quadratic curve below to the power function in the previous problem). Use regression to find a quadratic equation to model the data. Round the numbers in your equation to 3 decimal places. b) Use your equation to make a better prediction for the PCB concentration that you could expect in a 10 year old trout, round to the nearest tenth. Solutions: a) Enter into the calculator the data from the table, then select the quad option to generate the regression equation: y 0.130 x 2 0.351x 0.599 b) Using the equation from a), substitute 10 for x and solve for y. y 0.130 102 0.351 10 0.599 y 17.1 ppm Homework: 3, 7, 10, 11