Soon after taking an aspirin, a patient has absorbed 350 mg of the drug. If the amount of aspirin in the bloodstream decays exponentially, with half being removed every 2 hours, find the time it will take for the amount of aspirin in the bloodstream to decrease to 290 mg. Select the answer rounded to three decimal places.
A)1.843 hours
B)5.529 hours
C)0.921 hours
D)4.607 hours
E)3.686 hours

Question

Quizplus · Accepted Answer

The exponential decay formula is $A = P(0.5)^{\frac{t}{h}}$, where $A$ is the amount after time $t$, $P$ is the initial amount, $0.5$ represents the half-life decay rate, and $h$ is the half-life in hours. Here, $P = 350$ mg, $A = 290$ mg, and $h = 2$ hours. Plugging these values into the formula gives $290 = 350(0.5)^{\frac{t}{2}}$. Solving for $t$ gives approximately $1.843$ hours.

Soon After Taking an Aspirin, a Patient Has Absorbed 350