medication duration using the function of e through time lapse
problem D(h)=8e(up carrot)-0.31(h)
find med level at 1 hour- no problem 5.88mg. but every time I insert 4 for the 4 hours I get a larger number... much larger indicting the med level has gone up.
I am sure it is my bad math not the patient begining kidney failure. any help would be apprecitated.
bjm
When h = 4 I get D(4 = 2.315
must be the way you are entering the values for calculations on your calculator.
On mine, an old "Sharp", I did:
2ndF
ln
(±.31x4)
=
x
8
=
It helps to find the problem if you posted what you've got, even if the number is much larger.
If you are using a calculator, I suspect the "minus" sign before the 0.31 had been left out.
The given formula is:
D(h) = 8e-0.31h
For h=1, 5.87 is correct.
For h=4,
8e-0.31*4
=8e-1.24
=2.32
If the minus sign is left out, it would have given 27.64 instead.
To calculate the medication level at different time intervals, we can use the given function D(h) = 8e^(-0.31h), where h represents the time elapsed in hours.
Let's start by calculating the medication level at 1 hour. Plug in h = 1 into the equation:
D(1) = 8e^(-0.31 * 1)
D(1) = 8e^(-0.31)
D(1) ≈ 8 * 0.733
D(1) ≈ 5.864
So the medication level after 1 hour is approximately 5.864 mg, which matches the value you provided.
Coming to your question about the medication level after 4 hours, let's calculate it.
D(4) = 8e^(-0.31 * 4)
D(4) = 8e^(-1.24)
D(4) ≈ 8 * 0.289
D(4) ≈ 2.312
The medication level after 4 hours is approximately 2.312 mg.
It seems like you are getting a larger number when you input 4 hours. This might be due to a calculation mistake or misunderstanding of the results. Remember that as time increases, the exponential term (e^-0.31h) decreases, which results in a lower medication level.
If you are getting a larger number, double-check your calculation process to identify any errors.
Additionally, it's worth noting that medication levels can be influenced by various factors, including the individual's metabolism rate, kidney function, and other physiological factors. If you suspect any issues with the patient's kidney function, it would be best to consult a medical professional for proper evaluation and guidance.