A stirred-tank blending system can be described by a first-order transfer function between the exit composition x and the inlet composition x1 (both are mass fractions of solute): X1(s)X(s)=s+1K where K=0.4 (dimensionless) and =10min. When the blending system is at steady-state (x= 0.2 ), the dynamic behavior is tested by quickly adding a large amount of a radioactive tracer, thus approximating an impulse function with magnitude 1.5. a. Without taking the inverse Laplace transform, use the Initial Value Theorem to determine the value of x(0). b. Derive the exit composition response x(t) using inverse Laplace transforms. What is the value of x(0) ? c. How do your answers from Parts a and b compare