Question

example 9: ibuprofen metabolizes at a rate of about 29% decrease per hour. if you take a 500 mg dose of ibuprofen, how much will be left in your bloodstream after 4 hours, the time until you are allowed to take another dose? from this information, we know: - ( p_0=) mg - ( r = 29%), which means ( r = 0.29), which makes ( b = 0.71) - the problem involves exponential decay - where ( n=) # of hours after the dose is taken

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is \(P(n)=P_0\times b^n\), where \(P_0\) is the initial amount, \(b = 1 - r\) ( \(r\) is the rate of decay), and \(n\) is the number of time - periods.

Step2: Substitute the given values into the formula

We know that \(P_0 = 500\) mg (the initial dose of ibuprofen), \(b=0.71\) (since \(r = 0.29\) and \(b=1 - 0.29\)), and \(n = 4\) (the number of hours).
So, \(P(4)=500\times(0.71)^4\).
First, calculate \((0.71)^4=0.71\times0.71\times0.71\times0.71 = 0.25411681\).
Then, \(P(4)=500\times0.25411681\).
\(P(4)=127.058405\approx127.06\) mg.

Answer:

After 4 hours, approximately \(127.06\) mg of ibuprofen will be left in the bloodstream.