Q: Greenhouse Gases Carbon dioxide is a greenhouse gas in the atmosphere that ma
ID: 3103235 • Letter: Q
Question
Q: Greenhouse Gases Carbon dioxide is a greenhouse
gas in the atmosphere that may raise average temperatures
on Earth. The burning of fossil fuels could be
responsible for the increased levels of carbon dioxide. If
current trends continue, future concentrations of atmospheric
carbon dioxide in parts per million (ppm) could
reach the levels shown in the accompanying table. The
concentration in the year 2000 was greater than it
had been at any time in the previous 160,000 years.
Year 2000 2050 2100 2150 2200
CO2 (ppm) 364 467 600 769 987
(a) Let x be in years, x=0 where corresponds to
2000, x=1 to 2001, and so on. Find values for
C and a so that f(x)=Ca^x models the data.
(b) Graph f and the data in the same viewing rectangle.
(c) Use f(x) to estimate graphically the year when
the carbon dioxide concentration will be double
the preindustrial level of 280 ppm.
Explanation / Answer
(a) Since f(0) = C*a^(0) = C*1 = 364, we can conclude that C = 364.
We use the next point f(50) = 467 to find a:
467 = 364*a^50
a = (467/364)^(1/50) = about 1.005 or e^0.005
(b) The graph should look a bit like a J-shape.
(c) The graph should indicate that x=86 at the 560 ppm level (remember it said double 280 ppm). This would indicate the year 2086.
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