Q. 105 - Precalculus Enhanced with Graphing Utilities

Question

Drug Medication The function 

$D\left(h\right)=5e^{-0.4h}$

can be used to find the number of milligrams  of a certain drug that is in a patient's bloodstream  hours after the drug has been administered. How many milligrams will be present after 1 hour? After 6 hours? 

Step-by-Step Solution

Answer

$$\begin{gathered} D\left(1\right)=0.35mg \\ D\left(6\right)=0.45mg \end{gathered}$$

Step 1.Given information

Given drug medication function

$D\left(h\right)=5e^{-0.4h}$

Step 2.Determine the value of D ( 1 )

Substitute 1 for h in the given function. 

$$\begin{gathered} D\left(1\right)=5e^{(0.4)1} \\ =5e^{0.4} \\ =5(0.6703) \\ =3.35 \end{gathered}$$

So, a patient's bloodstream will have $3.35mm$ of the drug after 1 hour. 

Step 3.Determine the value of D ( 6 )

Replace h with 6 in the given function. 

$$\begin{gathered} D\left(6\right)=5e^{(0.4)6} \\ =5e^{-2.4} \\ =5(0.0907) \\ =0.45 \end{gathered}$$

Therefore, $0.45mg$ of the drug will be present in a patient's bloodstream after 6 hours.