A tank contains $1000$ litre of water in which $25$

$kg$ of salt is dissolved. Then, $50$ litres of brine,

containing cost$)kg$ of dissolved salt,

starts to run into the tank per minute. The

mixture, kept uniform by stirring, runs out at

the same rate.

a$)$ Find the amount of salt $y(t)$ in the tank at any time $t.$

$($Answer: $\{$:$y(t)==1+\frac{e^{-0\mathrm{.}1t}}{1002\mathrm{.}5}[(-0\mathrm{.}05cost+sint)]-0\mathrm{.}975e^{-0\mathrm{.}05t})$

b$)$ Sketch $y(t)$ as a function of time by hand.

c$)$ Find the amount of time required to double the salt content of the tank.