Single Variable Calculus, Chapter 1, 1.2, Section 1.2, Problem 11

A pharmacist use the equation $c = 0.0417D(a +1)$ to determine the appropriate
dosage $c$ for a child of age $a$, given that the recommended adult dosage
for a drug is D(in $mg$). Suppose the dosage for an adult is 200 mg.


(a.) Find the slope of the graph of $c$. What does it represent?


$
\begin{equation}
\begin{aligned}
c &= 0.0417 \, \, \, D(a+1) ; D=200\\
c &= 0.0417(200)(a + 1)\\
c &= 8.34(a + 1)\\
\end{aligned}
\end{equation}\\
\boxed{ 8.34, \text{slope represents the change in } mg \text{ for every 1 year change}}
$



(b.) Find the dosage for a newborn.


$
\begin{equation}
\begin{aligned}
c &= 8.34 (a + 1) ; a = 0 \text{ for new born}\\
c &= 8.34 (0 + 1)
\end{aligned}
\end{equation}\\
\boxed{c = 8.34 \, mg, \text{ dosage for new born}}
$