A tank whose time constant is $1$ min. It has an outlet pipe whose resistance to fluid circulation is $1/9$ foot$/($ft$3/$min$).$ Said tank is operating in a steady state with an inlet flow rate of $10$ ft$3/$min$.$ At one point the flow rate increases sharply to $100$ ft$3/$min$.$ for $0\mathrm{.}1$ min. adding $9$ ft$3$ of water evenly for the indicated time.

Represent the actual response of the tank and compare it with the response that would be obtained for an equivalent ideal boost.