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=0.567n + 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?
Concept Exercise: given the problem above, provide written responses to address the following points as precisely and thoroughly as possible.
1) Explain the problem in your own words.
2) What mathematical concepts learned in this module apply to this problem (equations and inequalities)?
3) Explain the steps you must take to solve this problem.
4) What is the most difficult aspect of solving this problem?
5) Explain exactly what the answer means from a mathematical perspective.
This explains how to use given formulas to solve a multi-step word problem, and then to explain the concepts in the word problem.