My Mom is so Cool

I realized we forgot to calculate the Tarceva that was already in my system. I could not figure it out quickly, so out of curiosity, I asked my mom at Midnight last night. I woke to this at 7AM.
From Barbara:
After each half life, the amt in your system is 1/2 of what it was 1 half life (36 hours) before.  So for the 100 mg which you took 16 days ago, the amt remaining after each half life is:
Day 0          100mg
Day 1  1/2    50mg
Day 3             25
Day 4 1/2    12.5
Day 6            6.25
Day 7 1/2    3.125
Day 9           1.56
Day 10 1/2   0.78
Day 12          0.39
Day 13 1/2    0.195
Day 15           0.1
Day 161/2      0.05
So:
The one you took 16 days ago would have about 0.07 mg reamining.
The one you took 15 days ago would have               0.1 mg remaining.
The one you took 14 days ago would have around 0.15 mg remaining.
”            ”             ”            13 ”       ”               ”    ”            ”                    0.26       ”
”           ”              ”            12                                                                     0.39
11                                                                      0.65
10                                                                      1.04
9                                                                       1.56
8                                                                       2.60
7                                                                        4.16
6                                                                        6.25
5                                                                       10.25
4                                                                        17
3                                                                       25
2                                                                       42 (c0rrected)
1                                                                        67
0                                                                      100
Total remaining is about                                        277 mg (corrected).

The amts remaining ofter days 3, 6, 9, 12, and 15 are exact.  I just interpolated linearly in between, so it is not exact.  It would be better to graph it on semi-log paper.  The biggest errors are for the last few days and those errors are much bigger than the amts remaining due to the earlier days that you can almost neglect the earlier days.  I think that the amts I have calcuated are an overestimate, since I assumed the amts remaining dropped linearly between the exact amts and they actually drop off exponentially.

A few days later: Clark found a formula on line for calculating the exact amts remaining each day.  Assuming that your 1  1/2 day half-life of tarceva is correct, if you take a 100 mg pill on day 0, then the amts remaining each integer day are:

Day 0    100mg

Day 1       63.0

Day 2      39.7

Day 3     25.0

Day 4     15.7

Day 5       9.9

Day 6       6.2

Day 7       3.9

Day 8       2.5

Day 9        1.6

Day 10     1.0

Day 11     0.6

Day 12    0.4

Day 13    0.25

Day 14    0.15

Day 15    0.1

Day 16    0.06

So, the one you took 16 days ago has about 0.06 remaining, the one you took 15 days ago has 0.1 , etc .  Add up the column, round to the neareast 0.1, and you get 270  mg remains including the 100mg that you took today.  If you didn’t take it today and for 6 days before that, there should be about 10 mg left in your system.

One thought on “My Mom is so Cool

  1. Tom Z & Dean L March 26, 2010 at 06:35 Reply

    I love this! It’s like when you’re a kid & ask your mom to untie the miserable knots in your yucky shoelaces: magic.
    I love math too (well, maybe not the super-hardcore stuff). See, Boys & Girls? It really DOES come in handy in Real Life.

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