Question 149272This question is from textbook College Algebra
: i) Problem: In 1960, the United States generated 87.1 million tons of municipal solid waste and recovered (recycled) only 4.3% of it. The amount of municipal solid waste generated in the United States can be modeled by the formula w = 3.14n + 87.1, while 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.
(1) Use the formulas to determine the year in which the United States generated over 100 million tons of municipal solid waste.
(2) Find the year in which 13% of the municipal solid waste generated will be recovered.
(3) Will the recovery rate ever reach 25%?
(4) According to this model, what is the maximum percentage of solid waste that will ever be recovered?
This question is from textbook College Algebra
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In 1960, the United States generated 87.1 million tons of municipal solid waste and recovered (recycled) only 4.3% of it. The amount of municipal solid waste generated in the United States can be modeled by the formula w = 3.14n + 87.1, while 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.
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w = 3.14n + 87.1
100 = 3.14n + 87.1
12.9 = 3.14n
n = 4.109
Year = 1960 + 4.109 means in the year 1965
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(2) Find the year in which 13% of the municipal solid waste generated will be recovered.
w = 0.576n + 3.78
13 = 0.576n + 3.78
0.576n = 12.22
n = 21.21..
Year = 1960 + 21.21 is in the year 1982
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(3) Will the recovery rate ever reach 25%?
25 = 0.576n + 3.78
21.22 = 0.576n
n = 36.85..
Year = 1960 + 36.85.. = 1997
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(4) According to this model, what is the maximum percentage of solid waste that will ever be recovered?
The maximum percentage would be 100
100 = 0.576n + 3.78
0.576n = 96.22
n = 167.05
Year = 1960+167.05 = the year 2028
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Cheers,
Stan H.
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