<PRE><B>Question 147629</B>
In 1960, the United States generated 87.1 million tons of municipal solid waste and recovered (recycled) only 4.3% of it.
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The amount of municipal solid waste generated in the United States can be modeled by the formula w = 3.14n + 87.1
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The amount recovered can be modeled by the formula w = 0.576n + 3.78, where w is in millions of tons and n is the number of years since 1960.
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(1) Use the formulas to determine the year in which the United States generated over 100 million tons of municipal solid waste.
100 = 3.14n + 87.1
3.14n = 12.9
n = 4.108 years
1960 + 4.108 = the year 1965
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(2) Find the year in which 13% of the municipal solid waste generated will be recovered.
EQUATION:
0.576n + 3.78 = 0.13(3.14n + 87.1)
0.576n + 3.78 = 0.4082n + 11.323
0.1678n = 7.543
n = 44.95
1960 = 44.95 is the year 2005
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(3) Will the recovery rate ever reach 25%? 
0.576n + 3.78 = ?(3.14n + 87.1)
No: The asymptote for (0.576n + 3.78) /(3.14n + 87.1) is 0.1834 or 18.34%
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(4) According to this model, what is the maximum percentage of solid waste that will ever be recovered? 
Ans: 18.34%

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