to produce a dilute solution of sugar for a bioreactor... two streams are continuously fed into a tank: - pure water, at rate qw[L/s] - sugar syrup with concentration cs= cs(t)[g/L] of sugar, at rate qs[L/s] the volume V[m3] of liquid in the tank is constant. a dynamic model of the concentration c=c(t)[g/L] of sugar in the output steam is: Vdtdc=qscs(qs+qw)c suppose the single input cs=cs(t) affects the output c=c(t), while qw and qs are constants. let Cs be the nominal steady-state value of the input cs(t). write an equation for c, the associated steady-state value of the output c(t), in terms of Cs. define deviation variables c(t):=c(t)c and cs(t):=cs(t)cs. write eqn. 1 in terms of these deviation variables. derive the transfer function G(s)=C(s)/Cs(s) governing the response of the output C(s):=L[c(t)] to the input Cs(s):=L[cs(t)], where L[] is the Laplace transform. write it in standard gain/time-constant form