I expect puality solveions for these problems. Fov mult show your work in order to receive credic. I am grading your work, not the answer! Be sure to write neraty, knep par eart organized, and dearly indicate your final enswer.

In $1991,$ the body of a man was found in melting snow in the Alps of Northern Italy. An examination of a tissue sample revealed that $46\%$ of the carbon$-14$ present in his body at the time of his death had decayed. The hall$-$life of carbon$-14$ is approal mately $5728$ years How long ago did this man die? $($Hint: Express the quantity of carbon$-14$ in the form $Q=Q_0{e}^{kt}$ and use the half$-$life to find $k$ first.$)$

A person's blood alcohol content $($BAC$)$ is a measure of how much alcohol is in the blood stream. When a person stops drinking, the BAC declines over time as the alcohol is metabolized. The BAC, $Q,$ of a person $4$ hours after the he stops drinking is given by

$Q=Q_0{e}^{-(\frac{t}{4})}.$

where $Q_0$ is the person's initial BAC and $a$ is known as the elimination time. How long does it take for a person's BAC to drop from $0\mathrm{.}10$ to $0\mathrm{.}04$ if the elimination time $a=2\mathrm{.}5$ hours?