Chapter 8.5, Problem 62E

a.

To determine

To write: a recursive rule for the amount of the drug in the blood stream after n dose.

Answer to Problem 62E

  $a_n=0.4a_{n-1}+325$ .

Explanation of Solution

Given:

A doctor prescribed 325 milligram drug every 8 hours for 10 days. And 60% of the drug is removed from the bloodstream every 8 hours.

Calculation:

Let $a_n$ is the amount of drug. Then

  $\begin{array}{l}{a}_1=325\\ a_n=0.4a_{n-1}+325\end{array}$

Hence, the amount of the drug in the blood stream after n dose is $a_n=0.4a_{n-1}+325$ .

b.

To determine

To check: that happens in the level of drugs given the prescribed dosage.

Answer to Problem 62E

  $a_{30}=0.4a_{30-1}+325=541.66$ .

Explanation of Solution

Given:

A doctor prescribed 325 milligram drug every 8 hours for 10 days. And 60% of the drug is removed from the bloodstream every 8 hours.

Calculation:

From part (a) $a_n=0.4a_{n-1}+325$

Therefore, $a_{30}=0.4a_{30-1}+325=541.66$

c.

To determine

To check: that happens in the level of drugs is doubled.

Answer to Problem 62E

  $a_{30}=1083.33$ .

Explanation of Solution

Given:

A doctor prescribed 325 milligram drug every 8 hours for 10 days. And 60% of the drug is removed from the bloodstream every 8 hours.

Calculation:

From part (a) $a_n=0.4a_{n-1}+325$

If the level of drugs is doubled, then $a_n=0.4a_{n-1}+650\left(2\times 325\right)$

Therefore, $a_{30}=0.4a_{30-1}+650=1083.33$