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# The following plasma concentrations (in ug/ml) of a new drug

The following plasma concentrations (in ug/ml) of a new drug were recorded in a patient. Is this data best fit by a single or double compartment model?

Time (hr) conc.
0.26 0.6149
0.51 0.4299
0.77 0.3213
1.02 0.2203
1.25 0.1773
1.51 0.1242
1.76 0.1167
2.02 0.0928
2.25 0.0722
2.51 0.0658
2.76 0.0614
3.02 0.0607
4.02 0.0471
5.01 0.0505
6.01 0.0438
7.01 0.0379
8.01 0.0325
9 0. 0305
10 0 .0282

From my understanding, you just need to either do a single exponential fit or a more complex exponential fit to see which fits the points better and determine single vs. double compartment model.

I think that if a single exponential does not fit, then a "best-fit" model is used, and it can be called a double compartment.

See attached file for full problem description.

#### Solution Preview

Please see the attached file.

Let C = concentration
t = time
If we use a single exponential fit then we could write:
C = aebt
I have done so in Excel but a ...

#### Solution Summary

The solution provides detailed explanations and answer in the attached files.

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