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# Modelling the amount of a drug in the bloodstream watch

1. Hi.

These are the records of the amount of a drug for treating malaria in the bloodstream over the ten hours following an initial dose of 10 nanograms:

Time (hour) Amount of drug in bloodstream (nanogram)

0 ... 10
0.5 ... 9
1 ... 8.3
1.5 ... 7.8
2 ... 7.2
2.5 ... 6.7
3 ... 6
3.5 ... 5.3
4 ... 5.2
4.5 ... 4.6
5 ... 4.4
5.5 ... 4
6 ... 3.7
6.5 ... 3
7 ... 2.8
7.5 ... 2.5
8 ... 2.5
8.5 ... 2.1
9 ... 1.9
9.5 ... 1.7
10 ... 1.5

PART A

1.Use this information to help you find a suitable function to model this data.
2. Draw a graph of your function and compare your graph to the values above, when graphed.
3. Comment on the suitability of your function

(these have been done)

PART B
-A patient is instructed to take 10 nanograms of this drug every six hours.

1. Sketch a diagram to show the amount of the drug in the bloodstream over a 24-hour period and state any assumptions made.

2. Use your GDC (graphic display calculator) or graphing software and your model from Part A to draw an accurate graph representing this situation.

3. State the maximum and minimum amounts during this period.

4. Describe what would happen to these values over the next week if:
a) no further doses are taken
b) doses continue to be taken every six hours.

Cogito, ergo IB.
2. The data you are given is for an initial dose. If you were to add this dose every six hours, you would be adding a new decay pattern to the original.

In other words, use the graph of the data you are given, and then every time a new dose of the drug is added, increase the values of the amount of drug left in the blood stream by the amount of the new dose of drug left in the blood stream.

For example: at the sixth hour, the drug content is 3.7ng. By adding a new dose of the drug, the drug content at the sixth hour is 13.7ng. At the seventh hour, the first dose of the drug decays to the seventh hour point, and the second dose of the drug decays to the first hour point. If you add the two, you will have the real seventh hour drug data, which is 2.8+8.3, or 11.1ng
3. I have the same problem too; i am stuck at "find a suitable function to model this data." I am thinking of a logarithmic function, but it doesn't seem to work. Help!
4. did you find the answer i am stuck with it now

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Updated: November 29, 2007
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