Data

The following data comes from the report on Population Growth and Carbon Dioxide Emissions directed by Anqing Shi of the Development Research Group at the World Bank. Here, I denotes global emissions of CO2 per year in gigatons and P denotes world population in billions of persons.

      Year         2000         2005             I         8.29         9.41             P         6.06         6.43

A model for global carbon dioxide emissions The following model is a slightly simplified version of the model developed by Dietz and Rozda in 1997. Here, I denotes global emissions of CO2 per year in gigatons and P denotes world population in billions of persons. Then, the model is: Ln(I)=a+bLn(P) For a and b constants to be determined. An assumption For the purpose of our work, we’ll assume that the yearly percentage increase in population is constant. Goals Your team’s objective is to predict the rate of change of global emissions of carbon dioxide in 2010. You will produce a report, which describes how you obtained your result. Your result will then be used later on to estimate the yearly increase of carbon dioxide in ppm. Calculation of Percentage Change in Population per Year Given that population percentage change is constant, we can find the yearly increase by doing the following: First look at the difference between population in 2005 and 2000. 6.43-6.06= 0.37 à we took initial population of 2005- population in 2000 0.37/6.43=0.5754 à the value we got can be divided by original population of 2000 in order to get the population growth over 5 years We can get the total population growth per year by dividing 0.5754/5=.0115085537 Therefore, the total population growth per year is 11.5% Given the values:

      Year         2000         2005             I         8.29         9.41             P         6.06         6.43

We can create 2 simultaneous equations through the base: Ln(I)=a+bLn(P) Ln(8.29)= a+bLn(6.06)= 2.115=a+1.802b Ln(9.41)=a+bLn(6.43)= 2.29=a+1.861b A=-1.703 B=125/59 a=ln(8.29)-b(ln6.06) b=ln(9.91)-a/ln(9.43) a= goal: take the function I and take the derivative of the function in 2010.