Modeling CO2 emissions a) Use the data from 1960 and 1990 to find a linear function that models the CO2 b) Use your linear function to predict the CO2 emissions in 2005. Compare your prediction with the actual CO2 emission in 2005

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Modeling CO2 emissions  a) Use the data from 1960 and 1990 to find a linear function that models the CO2  b) Use your linear function to predict the CO2 emissions in 2005. Compare your prediction with the actual CO2 emission in 2005

Cristiano Sears · Accepted Answer

a)  Let t represent years after 1960. , C=CO2 emissions.  Suppose the linear function that gives relation between the year and CO2 emissions be:  C=At+B−−−(1), Where A and B are constants.  Now we need to use data from year 1960 and 1990.  For Year 1960 :  t=0andC=316.9  substituting this in (1):  ⇒316.9=A(0)+B  ⇒B=316.9  For Year 1990 :  t=1990−1960=30andC=354.2  Substituting this in (1):  ⇒354.2=A(30)+316.9  ⇒37.3=A(30)  ⇒A=1.243  Hence on Substituting the value of A and B in (1),  ⇒C=1.243t+316.9  This is our linear function that models CO2 emissions with time.  b)  Now,  C=1.243t+316.9  Now we are given to predict the CO2 emissions in the year 2005  ⇒t=2005−1960=45  ⇒C=1.243(45)+316.9=372.85  According to our prediction, the CO2 emissions in 2005 is 372.85  But actually it is 379.7  Difference in Actual and Predicted value =379.7−372.85=6.85

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