Question

QE: Suppose we have this data on the amount of medicine in someone’s blood:

time        amount

0        0

1        0.151632665

2        0.367879441

4        0.541341133

6        0.448083615

8        0.293050222

10        0.168448675

16        0.021469608

24        0.000884767

Compute their total exposure to the medicine, which is the AUC (area-under-curve), from t=0 to 24.

If you are pasting this data set into a spreadsheet, it will probably get pasted all into one column instead of into two columns. To separate it out into two columns, highlight the data, then use the “Data” tab, select “Text to Columns”, tell it the data is Delimited, choose “next”, then click the box for “Space”, and it should show a new column divider to indicate how it will separate the columns once you hit “Finish”. Text-to-columns is a handy Excel skill!

Answer 1

The AUC (area-under-curve) can be determined using the formula:

Computing the area:

We get:

Time(x)	Amount (y)	(y1 + y0) / 2	(x1 - x0)	Area
0	0	0.075816333	1	0.075816
1	0.151632665	0.259756053	1	0.259756
2	0.367879441	0.454610287	2	0.909221
4	0.541341133	0.494712374	2	0.989425
6	0.448083615	0.370566919	2	0.741134
8	0.293050222	0.230749449	2	0.461499
10	0.168448675	0.094959142	6	0.569755
16	0.021469608	0.011177188	8	0.089418
24	0.000884767	SUM	4.096023

Hence, the AUC (area-under-curve), from t=0 to 24 is obtained as 4.096023