Question

The concentration C in milligrams per milliliter (mg/ml) of a certain drug in a person's blood-stream t hours after a pill is swallowed is modeled by C(t)=2+(3t/1+t^3)-e^-0.05t.estimate the change in

concentration when t changes from 30 to 40 minutes.

Answer 1

To estimate the change in concentration of a drug over 10 minutes, calculate the drug concentration function at 0.5 and 0.6667 hours and subtract the former value from the latter. This calculation is relevant to pharmacokinetics and drug dosing.

Step-by-step explanation:

The question asks us to estimate the change in concentration of a drug in the bloodstream as time increases from 30 minutes to 40 minutes. This involves calculating the values of the function C(t)=2+(3t/1+t^3)-e^-0.05t at t = 30 and t = 40 and subtracting the former from the latter. To clarify, convert the time from minutes to hours since the given function uses time in hours (30 minutes = 0.5 hours and 40 minutes = 0.6667 hours).

First, we calculate C(0.5) and C(0.6667). We then find the difference ΔC which is C(0.6667) - C(0.5). This difference represents the estimated change in drug concentration over the 10-minute interval.

The question is related to the concept of analyzing drug concentration over time, which is crucial for understanding pharmacokinetics and dosing in medical and health sciences. This mathematical approach provides important insights into how drugs interact with the body over time.