Calculator Models of Functions Vocabulary/Concepts/Skills: Regression Interpret constants, Extrapolate Residuals coefficients, bases Estimate Correlation Coefficient Interpolate (linear data) Predict Example 1: The data in the table shows the circulation in millions of USA Today from 1985 to 1993. Years are shown as the number of years since 1985. Years since 1985 0 1 2 3 4 5 6 7 8 Circulation 1.418 1.459 1.586 1.656 1.755 1.843 1.867 1.957 2.001 Use the first and last data points Number of Years Since Number of Subscribers to find an exponential model of 1970 (millions) the form for the data. How good 0 4.5 is the fit? 5 9.8 According to this model, what 10 16.0 is the estimated circulation in 2002? 14 29.0 Compare the estimate with the 16 37.5 actual circulation. What other 18 44.0 functions might model the data well? 20 50.0 Explain why another function is 22 53.0 more reasonable in the context of 24 55.3 the problem. Example 2: Shown is the number of cable television subscribers in the US for several years between 1970 and 1994. Years are expressed as number of years since 1970 and the number of subscriptions is given in millions. Look at a scatter plot of the data and decide on an appropriate function to model the data. The data appears to be leveling off. What in the context explains the leveling off? Looking at your equation model, what is the number to which the data levels off- i.e. what is the carrying capacity?
Calculator Models of Functions Vocabulary/Concepts/Skills: Regression Residuals Correlation Coefficient (linear data) Interpret constants, coefficients, bases Interpolate Extrapolate Estimate Predict Example 1: The data in the table shows the circulation in millions of USA Today from 1985 to 1993. Years are shown as the number of years since 1985. Years since 1985 0 1 2 3 4 5 6 7 8 Circulation 1.418 1.459 1.586 1.656 1.755 1.843 1.867 1.957 2.001 Number of Years Since 1970 Number of Subscribers (millions) 0 4.5 5 9.8 10 16.0 14 29.0 16 37.5 18 44.0 20 50.0 22 53.0 24 55.3 Use the first and last data points to find an exponential model of the form for the data. How good is the fit? According to this model, what is the estimated circulation in 2002? Compare the estimate with the actual circulation. What other functions might model the data well? Explain why another function is more reasonable in the context of the problem. Example 2: Shown is the number of cable television subscribers in the US for several years between 1970 and 1994. Years are expressed as number of years since 1970 and the number of subscriptions is given in millions. Look at a scatter plot of the data and decide on an appropriate function to model the data. The data appears to be leveling off. What in the context explains the leveling off? Looking at your equation model, what is the number to which the data levels off- i.e. what is the carrying capacity?
Precalculus_FullDocument_10.19.15.docx