Water $($H$2$O$($l$))$ flows into the heater$/$tank at the initial flow of $1\mathrm{.}5$ LTR$/$min$,$ the inflow of water grows steadily and doubles every $10$ min.

The water $($H$2$O$($l$))$ is boiled away from the heater$/$tank at an initial rate of $1\mathrm{.}1$ LTR$/$min but the boiling rate of water out of the heater$/$tank increases by $1\%$ every minute. Let the time t be in minutes.

a$)(5\%)$ Is the amount of water in the heater$/$tank a constant unstable curve? Justify

b$)(15\%)$ Write down the mass balance of the water inside the heater$/$tank using a differential balance. Write down all terms in the mass balance as a function of t$.$

c$)(15\%)$ How much water has accumulated in the heater$/$tank after $60$ minutes? Calculate by integrating differential balance