Chapter 1, Problem 63RE

a.

To determine

To find: the initial number of units of the drug administered.

Answer to Problem 63RE

The initial number of units of the drug administered is 90.

Explanation of Solution

Given information: A drug is administered intravenously for pain. The function $f\left(t\right)=90-52\ln \left(1+t\right),0\le t\le 4$ gives the number of units of the drug in the body after t hours.

Calculation:

The initial number of units of the drug administered is when t = 0, so substitute in t = 0 into the equation $f\left(t\right)=90-52\ln \left(1+t\right)$ ,gives:

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

Therefore, the initial number of units of the drug administered is 90.

b.

To determine

To find: how much is present after 2 hours.

Answer to Problem 63RE

  $f(2)\approx 32.8722\text{units}.$

Explanation of Solution

Given information: A drug is administered intravenously for pain. The function $f\left(t\right)=90-52\ln \left(1+t\right),0\le t\le 4$ gives the number of units of the drug in the body after t hours.

Calculation:

  $\begin{array}{c}f\left(t\right)=90-52\ln \left(1+t\right)\\ t=2\\ f(2)=90-52\ln (1+2)=90-52\ln (3)\approx 32.8722\\ f(2)\approx 32.8722\text{units}.\end{array}$

c.

To determine

To draw: the graph of f.

Answer to Problem 63RE

Explanation of Solution

Given information: A drug is administered intravenously for pain. The function $f\left(t\right)=90-52\ln \left(1+t\right),0\le t\le 4$ gives the number of units of the drug in the body after t hours.

Calculation:

The graph of the function $f\left(t\right)=90-52\ln \left(1+t\right)$ is shown below.