Question

You take a 325 milligram dosage of ibuprofen. During each subsequent hour, the amount of medication in your bloodstream decreases by about 29% each hour.

a. Write an exponential decay model giving the amount y (in milligrams) of ibuprofen in your bloodstream t hours the initial dose.

b. Estimate how long it takes for you to have 100 milligrams of ibuprofen in your bloodstream. Round your answer to the nearest tenth

Answer 1

a.
`y = 325(0.71)^t`

b. ≈ 3.44 hours

Explanation:

`a = 325\\r = 29%\\`

a.
`y = a(1-r)t\\\\y= 325(1-0.29)^t\\\\y = 325(0.71)^t`

b.
`100=325(0.71)^t\\\\t= 3.441426\\\\3.44 hours`