A body assimilates a 12-hour cold tablet at a rate modeled by $d C / d t = 8 - \ln \left( t ^ { 2 } - 2 t + 4 \right) , 0 \leq t \leq 12$ where $d C / d t$ is measured in milligrams per hour and $t$ is the time in hours. Use Simpson's Rule with $n = 8$ to estimate the total amount of the drug absorbed into the body during the 12 hours.
A) $\approx$ 58.915 mg
B) $\approx$ 68.915 mg
C) $\approx$ 38.915 mg
D) $\approx$ 48.915 mg
E) $\approx$ 78.915 mg

Question

Quizplus · Accepted Answer

Simpson's Rule, with $n = 8$ and the given function, provides an approximation for the integral, which represents the total drug absorption over 12 hours. The calculation involves evaluating the function at equally spaced intervals, applying the Simpson's Rule coefficients, and summing the results. The correct approximation is $\approx 58.915$ mg.

A Body Assimilates a 12-Hour Cold Tablet at a Rate dC/dt=8−ln⁡(t2−2t+4),0≤t≤12d C / d t = 8 - \ln \left( t ^ { 2 } - 2 t + 4 \right) , 0 \leq t \leq 12dC/dt=8−ln(t2−2t+4),0≤t≤12

A Body Assimilates a 12-Hour Cold Tablet at a Rate $d C / d t = 8 - \ln \left( t ^ { 2 } - 2 t + 4 \right) , 0 \leq t \leq 12$