Question 147629: 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?
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
--------------------------------
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.
100 = 3.14n + 87.1
3.14n = 12.9
n = 4.108 years
1960 + 4.108 = the year 1965
-----------------------------
(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
------------------
(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%
-----------------------------
(4) According to this model, what is the maximum percentage of solid waste that will ever be recovered?
Ans: 18.34%
|
|
|
