Half life question in matlab
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Metronidazole (used to treat infections) has a half life of H = 7.9 hours. Use solve to calculate [5 pt] the amount of time it takes for 50mg to decay to 20mg. Note that the decay constant is −ln(2)/H.
Can someone help me with the code that would be used to solve this type of problem?
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Answers (2)
Star Strider
on 29 Jan 2015
See the documentation for the solve function. The question itself has all the information you need otherwise. Particularly note ‘−ln(2)/H’.
The question assumes single-compartment kinetics for metronidazole, an anti-protozoal agent that is also active against C. dificile and some others.
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Star Strider
on 30 Jan 2015
For the record, the solution to this problem is quite simply:
syms C(t)
H = 7.9;
K = -log(2)/H;
C(t) = exp(K*t);
t20s = solve(C == 20/50, t);
t20d = vpa(t20s, 3)
giving:
t20d =
10.4
So the concentration has reached the 20mg level at 10.4 hours.
Roger Stafford
on 29 Jan 2015
Bradley, just ask yourself, "what power of 2 do I have to divide 50 by to get 20?". Then that power should be the ratio of the necessary decay time to 7.9 hours. It would be a very simple one-line matlab computation.
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Roger Stafford
on 30 Jan 2015
If you discard that incorrect minus sign, you've already solved your problem without using 'solve'. They ought to give you extra credit for that.
If you are determined to use 'solve', then go back a step and write the equation you were trying to solve before you took the logarithm.
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