A material M is imported into a country principally to manufacture one family of products with an…

A material M is imported into a country principally to
manufacture one family of products with an average life of _t years and a
growth rate of rc% per year. The material is not currently recycled at end of
life, but it could be. The government is concerned that imports should not
grow.

(a) What recycle fraction, fcrit, is necessary to make this
possible?

(b) The longer the average product life, _t, the
smaller is its fractional contribution to future supply. What is the limiting
life beyond which recycling cannot keep up with increased demand?