exponential decay

Question

You take a 325 milligram dosage of ibuprofen. During each hour, the amount on medication in your bloodstream decreases by about 29% each hour. Write an exponential decay model giving the amount y (in milligrams) of ibuprofen in your bloodstream t hours after the initial dose. Find and interpret the y-value when t=1.5.

 

About how long would it take for you to have 100 milligrams of ibuprofen in your bloodstream?

Answer 1

After 1 hour, you are left with (100 - 29)% = 71%

 

y(t) = 325 (0.71)^t

 

y(1.5) = 325 (0.71)^1.5 = 194.4

 

After 1.5 hours, only 194.4 milligrams remain.  

 

100 = 325 (0.71)^T

 

log(100/325) = T log(0.71)

 

T = log(100/325) / log(0.71) = 3.44 hours

 

It takes 3.44 hours for the initial amount to drop to 100 milligrams.