Question

bruce takes some medicine. the amount of medication in his bloodstream decreases by 15% every 6 hours. if bruce takes a dose of 220 milligrams of the medication, about how much medication will be in his bloodstream after 24 hours? (1 point) 115 milligrams 0.11 milligrams 4.5 milligrams 11,137,500 milligrams graphing calculator

Explanation:

Step1: Determine the number of 6 - hour intervals in 24 hours

Since the time period is 24 hours and each interval is 6 hours, we calculate the number of intervals \(n\) as \(n=\frac{24}{6} = 4\).

Step2: Identify the decay formula

The formula for exponential decay is \(A = P(1 - r)^n\), where \(A\) is the final amount, \(P\) is the initial amount, \(r\) is the rate of decay (as a decimal), and \(n\) is the number of time intervals. Here, \(P = 220\) milligrams, \(r=0.15\) (since 15% = 0.15), and \(n = 4\).

Step3: Substitute the values into the formula

First, calculate \((1 - r)=(1 - 0.15)=0.85\). Then, \(A=220\times(0.85)^{4}\).
Calculate \((0.85)^{4}=0.85\times0.85\times0.85\times0.85 = 0.52200625\).
Then, \(A = 220\times0.52200625=114.841375\approx115\) milligrams.

Answer:

115 milligrams (corresponding to the option "115 milligrams")