Exercise 1.2.15

Question

If the recommended adult dosage for a drug is $D$ (in mg), then to determine the appropriate dosage $c$ for a child of age $a$, pharmacists use the equation $c = 0.0417D(a + 1).$ Suppose the dosage for an adult is 200 mg. 
    \begin{enumerate}[label=(\alph*)]
        \item Find the slope of the graph of $c$. What does it represent?
        \item What is the dosage for a newborn?
    \end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
    \item To find the slope of the graph of $c$, we should represent the equation for $c$ as the equation of type $y=kx+b:$
    $$c=0.0417D(a+1)=8.34(a+1)=8.34a+8.34.$$
    Thus, the slope of the equation $c$ is equal to $8.34.$ It represents the rate of change of the appropriate dosage for a drug for a child with respect to the age $a.$
    \item Since a newborn child is $0$ years old, we have $a=0.$ For $a=0,$
    $$c=8.34\cdot 0+8.34=8.34\mathrm{~mg}.$$
\end{enumerate}

Exercise 1.2.15

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Exercise 1.2.15

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