Chapter 6.1, Problem 24E

a

To determine

Write an exponential decay model giving the amount $y$ (in milligram) of ibuprofen in bloodstream $t$ hours after the initial dose.

Answer to Problem 24E

The number of phone subscriber in 2008 is $261.80$

Explanation of Solution

Given information:

325 milligram dosage of ibuprofen taken during each subsequent hours, the amount of medication in bloodstream decrease buy about 29% each hours

The exponential decay model is $y=a{\left(1-r\right)}^t$

The exponential decay giving the amount $y$ (in milligram) of ibuprofen in bloodstream $t$ hours after the initial dose is

  $\begin{array}{l}y=a{\left(1-r\right)}^t\\ y=325{\left(1-0.29\right)}^t\\ y=325{\left(0.75\right)}^t\end{array}$

b

To determine

To estimate the how long it take to have 100 milligrams of ibuprofen in bloodstream.

Answer to Problem 24E

The time taken to have 100 milligrams of ibuprofen in bloodstream is 3.4 hours

Explanation of Solution

Given information:

325 milligram dosage of ibuprofen taken during each subsequent hours, the amount of medication in bloodstream decrease buy about 29% each hours.

Use the trace feature of a graphing calculator to determine that $y=100$ when $t=3.4$ . After 3.4 hours to have the 100 milligrams of ibuprofen in bloodstream

  

Hence, the time taken to have 100 milligrams of ibuprofen in bloodstream is 3.4 hours.