Question 460201
Year 2000 2050 2100 2150 2200
CO2(ppm) 364 467 600 769 987
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(0,364),(50,467),(100,600),(150,769),(200,987)
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a) Let x be in yrs, where x=0 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.
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Using (0,364): 364 = C*a^0
C = 364
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Using (100,600): 600 = 364*a^50
a = 1.65^(1/50)
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f(x) = 364*(1.65)^(x/50)
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b) Graph f and the data in the same viewing rectangle.
{{{graph(400,300,-10,10,-10,800,354*1.65^(x/50))}}}
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c) Use f(x) to estimate graphically the year when the carbon dioxide concentration will be double the preindustrial level of 280 ppm. 
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Solve for "x":
560 = 354*1.65^(x/50)
1.58 = 1.65^(x/50)
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x/50 = log(1.58)/log(1.65)
x/50 = 0.91
x = 45.67
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Year = 2046
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Cheers,
Stan H.