In a beer factory, the waste water is being heated by a heat exchanger. The temperature of

the heating water is $45C$ and its flow rate is $25\frac{m^3}{h}.$ The inlet temperature of waste water

recorded as $10C$ and its flow rate is $30\frac{m^3}{h}.$

a$)$ Calculate $K$ and $$ values for this heating system.

b$)$ If the temperature of heating water is increased to $55C$ at $t=0,$ what will be the response

equation of the output variable, $y(t)=?$

c$)$ What will be outlet temperature of waste water at $5.$ hour?