After taking a medication its concentration in the bloodstream behaves as shown in the graph 650x/(x^3+200), where the x values are hours since first taking the medication and y is the concentration of the medication (mg/cc) in the blood stream after the given number of hours. The time x = 0 occurs at Monday 8:00 a.m.
Identify the sources of error and explain whether or not we can we compensate for them.
To identify the sources of error in this situation, we need more information about how the medication concentration was measured and any potential factors that could influence accuracy.
1. Measurement error: It is possible that there could be errors in the measurement of the medication concentration in the bloodstream, which could result in inaccurate data points on the graph. This can be due to limitations of the measurement technique, equipment malfunctions, or human error during the measurement process. To compensate for this error, it would be important to use reliable measurement techniques, calibrate equipment regularly, and ensure that measurements are taken with precision and accuracy.
2. Individual variation: Different individuals may metabolize the medication at different rates, which can lead to variations in medication concentration in the bloodstream. Factors such as age, weight, metabolism, liver function, and other medications being taken concurrently can influence the pharmacokinetics of the drug. To compensate for this variation, it is essential to consider individual patient characteristics while analyzing the data. A larger sample size with a diverse population can also help account for individual variations.
3. Dosage timing and adherence: In the graph provided, it is assumed that the medication was taken consistently at the prescribed intervals. However, in real-life scenarios, patients may not strictly adhere to the dosing schedule, leading to variations in the concentration of the medication in the bloodstream. To compensate for this error, it is crucial to gather accurate information on dosing times and patient adherence. Patient education and reminders can be helpful in maintaining proper medication adherence.
4. Model assumptions: The graph given assumes a specific mathematical model for the concentration of the medication in the bloodstream. If the model does not accurately represent the actual behavior of the medication in the body, there could be errors in the predicted concentrations. To compensate for this, one can consider using alternative models or refine the existing model based on empirical data to better fit the observed concentration values.
It's important to note that without explicit information about how the medication concentration was measured and other relevant details, it is difficult to provide a comprehensive analysis of potential error sources. Consulting with medical professionals and conducting thorough research specific to the medication and measurement techniques would be necessary to obtain a more precise assessment.