Chapter 3.5, Problem 38E

Recycling aluminum cans. It is known that 45% of all aluminum cans distributed are recycled each year. A beverage company uses 250,000 lb of aluminum cans. After recycling, the amount of aluminum, in pounds, still in use after t years is given by

$N\left(t\right)=250,000{\left(0.45\right)}^t$.

(Source: The Container Recycling institute.)

a. Find $N\text{'}\left(t\right)$.

b. Interpret the meaning of $N\text{'}\left(t\right)$.