Total emissions of carbon dioxide from the burning of fossil

Total emissions of carbon dioxide from the burning of fossil fuels have been increasing at about 33% per year (data from 2010 to 2011). If emissions continue to increase at this rate, about how much higher will total emissions be in 2050 than in 2010?Using the approximate formula, emissions will increase by a factor of nothing between 2010 and2050. Using the exact formula, emissions will increase by a factor of nothing between 2010 and 2050.

Solution

Let n represent the nth starting from 2010

Since emissions of carbon dioxide are increasing at rate 33% every year:

y_n+1 = y_n + 0.33y_n

=> y_n+1 = 1.33y_n

=> y_n+2 = 1.33y_n+1 = 1.33²y_n

=> y_n+3 = 1.33y_n+2 = 1.33³y_n

Since y_n represents 2010, y_n+1 represents the year 2011, y_n+40 will represent the year 2050)

Following the pattern of equations: y_n+40 = 1.33⁴⁰y_n

=> y_n+40 = 89963.354 y_n

In 2050, the emissions would increase by 8996335.4% as compared to 2010