In$2012,34\mathrm{.}1\%$ of all glass containers were recycled. A beverage company used

$150$ comma $000150,000$

lb of glass containers per year. After$$ recycling, the amount of$$ glass, in$$ pounds, still in use after t years is given by

Upper N left parenthesis t right parenthesis equals $150$ comma $000$ left parenthesis $0\mathrm{.}253$ right parenthesis Superscript tN$($t$)=150,000(0\mathrm{.}253)$t$.$

$$a$)$ Find

Upper N left parenthesis $5$ right parenthesisN$(5),$

and explain its meaning.

$$b$)$ Find

Upper N prime left parenthesis $5$ right parenthesisN$(5),$

and explain its meaning.

$$c$)$ When will

$44\%$

of the original amount of glass still be in$$ use?