answer 7, 8 ,9 10 and part 3

Mathematical Characterization of Model Equations

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• 7-For the model equations for Evans Blue, inulin and antipyrine, state their (i) dynamic order, (ii) whether they are linear/nonlinear, (iii) time-varying or time-invariant, and (iv) autonomous parts of the model equations. Explain your reasoning.
• 8-In a linear system, what should happen to the output if you double the input? Design an experiment to test whether or not the inulin model is linear. Present your rationale and provide results of the experiment to support your conclusion. Provide your results and do not forget to label your graphs with units and titles.
• 9-In a time-invariant system, if the input is offset by a time (i.e., delayed), what should happen to the output? Design an experiment to test whether or not the antipyrine model is time-invariant. Present your rationale and provide results of the experiment to support your conclusion. Provide your results and do not forget to label your graphs with units and titles.
• 10- On the basis of the inulin model equation and the continuous infusion protocol, provide qualitative answers to the questions in the following table. Specifically, predict what would happen following each of the perturbations listed in the table, with respect to the nominal condition specified earlier. Valid responses are: increased (I), decreased (D), unchanged (U), or insufficient information (IS).