Modeling displaystyle{C}{O}_{{2}} emissions a) Use the data from 1960 and 1990 to find a linear function that models the displaystyle{C}{O}_{{2}} b) U

generals336 2021-01-23 Answered
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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Expert Answer

Cristiano Sears
Answered 2021-01-24 Author has 96 answers
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=19901960=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=20051960=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 =379.7372.85=6.85
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