Question: Part a.) After a dose, the concentration of medication in the blood declines due to metabolic processes.

The half-life of a medication is the time required after an initial dosage for the concentration to be reduced by one-half.

A common model for this process is:

C(t)=C(0)e^(-kt)

where C(0) is the initial concentration, t is time in hours, and k is called the elimination rate constant, which varies among individuals. For a particular bronchodilator, k has been estimated to be in the range 0.047 to 0.107 per hour.

Part 1: Find an expression for the half-life in terms of k, and obtain a plot of the half-life versus k for the indicated range.

Part 2: If the concentration is initially zero and a constant delivery rate is started and maintained, the concentration as a function of time is described by

C(t)=(a/k)(1-e^(-kt))

where a is a constant that depends on the delivery rate. Plot the concentration after 1hr, c(1), versus k for the case where a=1 and k is in the range .047<=k 107="" per="" hour="" p="">

Please put the command for MATLAB to answer this problem and show step by step what you are doing. Please show me all the working and provide the answer.