In modeling the process of drug ingestion, distribution and subsequent metabolism in an individual, a simplified mathematical model was derived to be the following: = -kx+u kizi-k dzy dt dra dt y = where, , r and u are respectively the drug mass in the Gastrointestinal tract (GIT), the drug mass in the Bloodstream (BS), and the drug ingestion rate. All variables are expressed as deviations from their initial steady-state values. For a given small mammal used in a toxicology laboratory, the values of the effective "rate constants" associated with drug distribution into the blood stream and with drug elimination from the bloodstream were found respectively to be: k= 5.63 (min-), k= 12.62 (min)-, u(t) 1. (10 points) What are the eigenvalues of this dynamical system? 2. (10 points) What is the transfer function relating drug ingestion rate to the drug mass in the GIT and BS? 3. (10 points) What are poles and zeros of this transfer function? 4. (10 points) Obtain the dynamic response of the drug mass in the blood stream, 12, to a drug ingestion program which is given by 0 mg/min, 10 mg/min, 0 mg/min, t 5 min 5. (10 points) Repeat part (4) when the drug ingestion program is given by t