Prob. 7 (15 pts.) A stirred tank is operating in steady state with an inlet concentration =1. As a result of the assumption of steady state, the outlet concentration is also =1. (CLO3) As a result of a problem elsewhere in the chemical plant, it is necessary to ramp the concentration down to zero in a controlled fashion. Let t=0 be the time that the ramp starts. Then the inlet concentration is given by cin(t)=(1t)+u1t, where u1 is the Heaviside function. (a) Draw a sketch of the two functions making up cinin(t). (b) The equation governing the outlet concentration for t>0 is dc/dt+c=(1t)+u1t;c(0)=1 Solve for c(t) using Laplace transforms. Hint\#1 Don't forget to apply the initial condition. Hint \#2: You should refer to entry \#3 in the handout of common Laplace transforms. In addition, you may use an online resource to invert any transforms that arise