Codeine phosphate is a drug used as a painkiller. A common brand contains 30 mg of codeine. Samples of blood were taken at regular time intervals from a patient who had taken a pill containing 30 mg of codeine. The amount of codeine in the bloodstream was determined every 30 min for 3 h. The data are shown in the table below.

Question

Time After Consumption (min): 30, 60, 90, 120, 150, 180
Amount of Codeine in Blood (mg): 27.0, 23.5, 21.2, 18.7, 16.6, 14.5

I figured out the answers for parts a, b and c, but I need help with part d and e.

a) Create a scatter plot of the data and determine a suitable equation to model the amount of codeine in the bloodstream t min after taking the pill. Justify your choice of models.

b) Use the model to determine the instantaneous rate of change in the amount of codeine at each time given in the chart. How does it relate to the amount of codeine in the blood?

c) It is recommended that a second pill be taken when 90% of the codeine is eliminated from the body. When would this occur?

d) Assume that the same model applies to the second pill as to the first. Suppose the patient took a second pill one hour after consuming the first pill.

• Create a model for the amount of codeine in the patient’s bloodstream t min after taking the first pill.

• Determine the maximum amount of codeine in the patient’s bloodstream.

• Determine when 90% of the maximum amount would be eliminated from the body.

e) If the patient were to delay taking the second pill, how would it affect the results from part d)?

Answer 1

The 2nd pill is shifted by 60 minutes.

So, if the 1st pill is modeled by f(x), the 2nd pill will be modeled by f(x-t).

Now just work with the new f(x).