Question 149272
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.
-----------------------
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
------------------------------------------------

(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
-----------------------------------------
(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
=====================================
(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
==================================
Cheers,
Stan H.