# Body's response to a bolus injection of antibiotic

This model is used to 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

I'm not sure how to use the normal equations in MATLAB to plot this? We're not supposed to use polyfit function... I think you have to make a 2 column matrix with a column of 1's and a column of the time?

See attached file for full problem description.

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This model is used to 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 ...

#### Solution Summary

The solution provides a detailed and step-by-step explanation (incl. graphs from MATLAB) for the problem.