The eccentricity of the conic section
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Answer:
0.2225 gr/mile
Step-by-step explanation:
Let's work out first the amount of CO sent out in 1990.
The population we estimated in 12.5 million people with a total of driven miles per year of about
12.5 million*8,700 = 108,750 million miles.
With an CO emission factor of 0.9 g per mile, we would have a total of CO emitted rounding 0.9*180,750 = 97,875 million grams
Now, we must estimate the population for 2020.
Since we are assuming an exponential growth, the population in year t is given by a function
where C and k are constants to be determined.
We can take 1980 as year 0. This way calculations are lighter. 1990 is year 10 and 2020 is year 20.
So P(0) = 10.3 and C=10.3
So far we have
Given that P(10)=12.5
And the function that models the population growth is
We need P(20)
If the miles driven per person per year remains constant at 8700 mi/yr.person, then we have a total miles driven of
15.17*8,700=131,979 million miles, so the CO emitted would be 0.9*131,979=118,781.1 million grams.
The 30% of the CO sent out in 1990 is 0.3*97,875=29,362.5 million grams.
We must reduce 118,781.1 down to 29,362.5
Hence the new CO emission factor would be
29,362.5/131,979 = 0.2225 gr/mile