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: \(750 \mathrm{mg}\) Time: after 5 hours

Short answer

After 5 hours, there will be 240mg of aspirin left in the person's bloodstream.

Step-by-step solution

Understand the given

The person has taken a dosage of 750mg of aspirin. After 5 hours, we need to find out how much aspirin remains in their bloodstream. We have been given the formula to calculate the same: \(y=A(0.8)^{t}\), where \(y\) represents the concentration of aspirin, \(A\) represents the dosage taken, and \(t\) represents the hours since the dosage was taken.

Substitute the known values into the equation

We substitute \(A=750\) and \(t=5\) into the formula. So, we get: \( y =750(0.8)^{5} \).

Perform the calculation

We now perform the computation: \(750 \times 0.8^5 = 240 \).