Answer to Question #257231 in Calculus for JerryKim

Question

In this assignment, you are asked to write a matlab program to solve the following open ended problem, and submit the program and written summary including methods employed, algorithm implementation, final results and recommendations on further improvement.

Background

A drug administered to a patient produces a concentration in the blood stream given by

                                               C(t)=Atexp(-t/3 )

Where c is in milligrams per millimeter, t is in hours and A is injected units. For a given drug the maximum safe concentration (in mg/ml) is denoted as c_max, and the critical concentration(in mg/ml), denoted as c_critical, is the concentration below which an additional amount of drug needs to be administered to the patient.

a.      Determine how the injected unit A affects the maximum safe concentration and when the maximum safe concentration occurs.

b.      Determine how the ratio between c_critical and c_max affects the duration between the first and the second injections.

Suggestions

Answer 1

a.

$C'(t)=Ae^{-t/3}-Ate^{-t/3}/3=0$

$1-t/3=0$

$t=3$ hours

$C_{max}=C(3)=3A/e=1.1A$

b.

$C_{critical}=te^{-t/3}$

$C_{max}=2\cdot 1.1=2.2$

$C_{critical}/C_{max}=te^{-t/3}/2.2$