"In April 2007, Canada's Environment Minister John Baird announced new targets to reduce Canada's GHG emissions to 20% below the 2006 level by 2020, and to 60-70% below the 2006 level by 2050."This would leave Canada's emissions about 2% above the 1990 level in 2020 and would reduce them to [about 55.5%] below the 1990 level by 2050."
[Source: http://climate.pembina.org/issues/longer-term-targets]
Directions: Let B=the 2006 emissions level for Canada, and let A be the 1990 emission level.
(a) Explain why the first statement implies that (0.8)B = (1.02)A
(b) Solve for B in terms of A; that is, find a constant k such that B=kA
(c) Now carry out steps similar to those in (a) and (b) above, only base your equations on the assertion that "..and would reduce them to [about 55.5%] below the 1990 level by 2050" part, until you again obtain B=qA for some constant q
(d) How close are k and q?
Solution: Let B=the 2006 emissions level Let A be the 1990 emission level. Then (20% below B) = (2% above A) (0.8)B = (1.02)A B = [(1.02)/(0.8)]A B = (1.275 )A Using the other two figures: (about 65% below B) = (about 55.5% below A) (0.35)B = (0.445)A B = [(0.445)/(0.35)]A B = 1.271 A The match is close enough