I did this very approximately and not to the level of detail asked for in the book.
We'll just use the formula given in the book for Problems in Context, #5:
(Whoever used this formula in class to get N for the year 1995 and got a negative number ust have made a mistake.)N = 2.45 * Year -4,734
So our raw data (organized in decades) using this formula is (and I truncated so this is just an estimate):
t0 | t1 | t2 | t3 | t4 | ||
Year | 1995 | 2005 | 2015 | 2025 | 2035 | |
N | 153 | 178 | 202 | 227 | ||
CO2 | 918 | 1068 | 1212 | 1362 | ||
Change | 150 | 144 | 150 |
Here is the equations I used (multiplying by 6 as the book says for the carbon dioxide per car):
And it looks like the difference is "about" 150. So:
t0 = 918 tn = tn-1 + 150
Since I used decades from 1995, I'll look at what's going on in 2045 (instead of 2050 as in the book). This will be t5:
2045 (t5) = t4 + 150 = t3 + 150 + 150 = 1362 + 150 + 150 = 1662
Now we want the total CO2 added to the atmosphere, from 1995 to 2045. This is a sum:
Elaborating as we did in class to expose the pattern:Sum_0 = t0 Sum_1 = t0 + t1 Sum_2 = t0 + t1 + t2
For Sum_5 (ie 2045) = 918 * 6 + 150 * 5 * 6 / 2 = 7758Sum_0 = 918 Sum_1 = 918 + 918 + 150 Sum_2 = 918 + 918 + 150 + 918 + 150 + 150 OR Sum_n = 918 * (n+1) + 150 * (1 + 2 + ... + n) = 918 * (n+1) * 150 * (n)(n+1)/2