380- 370- 360- 350+ 340+ 1980 1985 1990 1995 2000 2005 ++ 2010 Video Example EXAMPLE 3 The linear equation C = 1.65429t2938.07 models the average CO₂, carbon dioxide, level (measured in parts per million) in the atmosphere at an observatory from 1980 to 2008. Use the linear model to estimate the average CO₂ level for 1995 and to predict the level for the year 2019. According to this model, when will the CO₂ level exceed 430 parts per million? SOLUTION Using C = 1.65429t2938.07 with t= 1995, we estimate that the average CO₂ level in 1995 was C(1995) = 1.65429 5429( (rounded to two decimal places). This is an example of interpolation because we have estimated a value between observed values. With t=2019, we get C(2019) = 1.65429 (rounded to two decimal places). So we predict the average CO₂ level in the year 2019 will be ppm (rounded to two decimal places). This is an example of extrapolation because we have predicted a value outside the region of observations. Consequently, we are far less certain about the accuracy of our prediction. 2938.07 - 2938.07% Using C = 1.65429t2938.07, we see that the CO₂ level exceeds 430 ppm when 1.65429t2938.07 > 430. Solving this inequality, we get t> (rounded to two decimal places). 1.65429 We therefore predict that the CO₂ level will exceed 430 ppm in the year . This prediction is risky because it involves a time quite remote from our observations. In fact, we see from the figure that the trend has been for CO₂ levels to increase rather more rapidly in recent years, so the level might exceed 430 ppm well before
380- 370- 360- 350+ 340+ 1980 1985 1990 1995 2000 2005 ++ 2010 Video Example EXAMPLE 3 The linear equation C = 1.65429t2938.07 models the average CO₂, carbon dioxide, level (measured in parts per million) in the atmosphere at an observatory from 1980 to 2008. Use the linear model to estimate the average CO₂ level for 1995 and to predict the level for the year 2019. According to this model, when will the CO₂ level exceed 430 parts per million? SOLUTION Using C = 1.65429t2938.07 with t= 1995, we estimate that the average CO₂ level in 1995 was C(1995) = 1.65429 5429( (rounded to two decimal places). This is an example of interpolation because we have estimated a value between observed values. With t=2019, we get C(2019) = 1.65429 (rounded to two decimal places). So we predict the average CO₂ level in the year 2019 will be ppm (rounded to two decimal places). This is an example of extrapolation because we have predicted a value outside the region of observations. Consequently, we are far less certain about the accuracy of our prediction. 2938.07 - 2938.07% Using C = 1.65429t2938.07, we see that the CO₂ level exceeds 430 ppm when 1.65429t2938.07 > 430. Solving this inequality, we get t> (rounded to two decimal places). 1.65429 We therefore predict that the CO₂ level will exceed 430 ppm in the year . This prediction is risky because it involves a time quite remote from our observations. In fact, we see from the figure that the trend has been for CO₂ levels to increase rather more rapidly in recent years, so the level might exceed 430 ppm well before
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.FOM: Focus On Modeling: Fitting Lines To Data
Problem 4P
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