Qwest Airlines has implemented a program to recycle all plastic drink cups used on their aircraft. Their goal is to generate $$5$ million by the end of the recycle program$$s five$-$year life. Each recycled cup can be sold for $$0\mathrm{.}005(1/2$ cent$).(4\mathrm{.}7)$

How many cups must be recycled annually to meet this goal? Assume uniform annual plastic cup usage and a $0\%$ interest rate.

Repeat Part $($a$)$ when the annual interest rate is $15\%.$

Why is the answer to Part $($b$)$ less than the answer to Part $($a$)?$