Question

Use the following information. The concentration of aspirin in a person's bloodstream can be modeled by the equation \(y=A(0.8)^{t},\) where \(y\) represents the concentration of aspirin in a person's bloodstream in milligrams (mg), \(A\) represents the amount of aspirin taken, and \(t\) represents the number of hours since the medication was taken. Find the amount of aspirin remaining in a person's bloodstream at the given dosage. Dosage: \(250 \mathrm{mg}\) Time: after 2 hours

Short answer

The amount of aspirin remaining in the person's bloodstream after 2 hours is approximately 160mg.

Step-by-step solution

Interpret the given variables

First, interpret what each variable in the equation represents: \(y\) represents the concentration of aspirin in a person's bloodstream in milligrams (mg), \(A\) represents the amount of aspirin taken, and \(t\) represents the number of hours since the medication was taken. In this problem, \(A=250mg\) (dosage) and \(t=2\) hours (time).

Substitute the values into the equation

Next, replace the variables A and t with the given values in the model equation: \(y = A(0.8)^t\) becomes \(y = 250(0.8)^2\).

Calculate the concentration

Calculate the value of \(y\), which represents the concentration of aspirin in the bloodstream after 2 hours. You compute this by multiplying 250 by 0.8 squared. This results in \(y \approx 160mg\).