Pr$2.[20$ Pts$]$ The voltage $v(t)$ across a device and the current $i(t)$ through it are $($where $t$ in

$sec$ Volt

and $i(t)=10$tmA

Possible integrals to be used:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}kdx=kx+C,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xdx=(\frac{1}{2})x^2+C$

a$)$ Calculate the voltage$-$and the current at $t=2$min.

b$)$ Calculate the total charge in the device from $t=0sec$ to $2$ sec $.$

c$)$ The power consumed by the device at $t=2sec.$

d$)$ Write the equation that we can use to calculate the energy $($electricity$)$ consumed by the device from $t=0$ to $2$ min and plug in numbers. Don't need calculate. Assuming your house $AC$ unit runs $2$ hours a day, $30$ days a month. Its power rating is $12000$ W $,$ the unit price for the electricity is $$0\mathrm{.}1$ KWH$,$ calculate how much money your $AC$ will use in this month.