$10$ points

$(7)$ A certain pain relieving drug must never exceed $3000$ mg in the body. The decay rate for the drug is $0\mathrm{.}065m\frac{g}{h}$our. If the dose size is $1000$ mg $,$ how many hours should pass between each dose $($round accordingly$)?$

$\frac{1,000}{1-e^{-0\mathrm{.}1T}}3000$

$\frac{1-e^{-0\mathrm{.}1T}}{1\mathrm{.}000}\frac{1}{3000}$

$1-e^{-0\mathrm{.}1T}\frac{1}{3}$

$-e^{-0\mathrm{.}1T}-1+\frac{1}{3}$

$-e^{-0\mathrm{.}1t}\frac{-2}{3}$

$10$ points

$(8)$ Given: $A={\left[\begin{array}{c}2\\ 0\\ 7\end{array}\right]}_{31},B=\left[\begin{array}{c}1\\ -3\\ 2\end{array}\right]$

$T\frac{ln(\frac{2}{3})}{0\mathrm{.}1}$

$T\frac{0\mathrm{.}40545108}{0\mathrm{.}1}N$

$T\frac{0\mathrm{.}405455108}{0\mathrm{.}1}4$ hours

Find: $2A-3B$

$2A=\left[\begin{array}{c}4\\ 0\\ 14\end{array}\right]-\left[\begin{array}{c}-3\\ 9\\ -6\end{array}\right]=\left[\begin{array}{c}1\\ 9\\ 20\end{array}\right]$