example 9: ibuprofen metabolizes at a rate of about 29% decrease per hour. if you take a 500 mg dose of…

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

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

Answer

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.