SOLUTION: Carbon dioxide (CO2) 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 o

Question 460201: Carbon dioxide (CO2) 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 CO2 concentration in the year 2000 was greater than it had been at anytime in the previous 160,000 years.
Year 2000 2050 2100 2150 2200
CO2(ppm) 364 467 600 769 987
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.
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.
This is a difficult one. Please assist me with this.
Thank you in advance Raven
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
----
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)
----
f(x) = 364*(1.65)^(x/50)
=============================
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.
------
Solve for "x":
560 = 354*1.65^(x/50)
1.58 = 1.65^(x/50)
---
x/50 = log(1.58)/log(1.65)
x/50 = 0.91
x = 45.67
------
Year = 2046
=======================
Cheers,
Stan H.
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