Analyze the body response to a bolus injection

Question

Assignment:

Analyze the body's response to a bolus injection of this antibiotic:

                                    B(t) = B₀e^(-k*t)

Using this model, and data provided for the average plasma concentration data in ug/ml with time in hours :

a) perform linear regression on this penicillin clearance using the normal equations

b) plot the concentration data and re-plot the log of the concentration data to show that it appears linear.

c) Determine initial concentration, B₀, and elimination rate constant, k

Concentration (ug/ml)	Time (min)
89	22
60	44
30	88
15	132
7	176

a) for linear regression

 ln( B ) = ln( B₀ )- Kt