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.


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