Chapter 0, Problem 63RE

(a)

To determine

To calculate : The units of the drug that were initially administered.

Answer to Problem 63RE

The drug initially administered is $90$ units.

Explanation of Solution

Given information :

A drug is administered intravenously for pain. The function given below gives the number of units of the drug in the body after $t$ hours.

  $f\left(t\right)=90-52\ln \left(1+t\right),0\le t\le 4$

Calculation:

Consider the function $f\left(t\right)=90-52\ln \left(1+t\right)$

To find the units of the drug that were initially administered, take $t=0$

  $\begin{array}{c}f\left(0\right)=90-52\ln \left(1+0\right)\\ =90-52\left(0\right)\\ =90\end{array}$

(b)

To determine

To calculate : The units of drug present after two hours.

Answer to Problem 63RE

The drug present after two hours is $32.87$ units.

Explanation of Solution

Given information :

A drug is administered intravenously for pain. The function given below gives the number of units of the drug in the body after $t$ hours.

  $f\left(t\right)=90-52\ln \left(1+t\right),0\le t\le 4$

Calculation:

Consider the function $f\left(t\right)=90-52\ln \left(1+t\right)$

To find the units of drug present after two hours, take $t=2$

  $\begin{array}{c}f\left(2\right)=90-52\ln \left(1+2\right)\\ =90-52\ln 3\\ \approx 32.87\end{array}$

(c)

To determine

To graph : The given function.

Explanation of Solution

Given information :

A drug is administered intravenously for pain. The function given below gives the number of units of the drug in the body after $t$ hours.

  $f\left(t\right)=92-52\ln \left(1+t\right),0\le t\le 4$

Graph:

  

Interpretation:

The domain is $\left[0,4\right]$ and the range is $\left[-20,100\right]$ .