Question

tutorial exercise
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 300 mg.
(a) find the slope of the graph of ( c ). what does it represent?
(b) what is the dosage for a newborn?

Explanation:

Step1: Substitute D=300 into equation

First, substitute the given adult dosage $D=300$ mg into the formula $c = 0.0417D(a + 1)$ to get the equation for child dosage in terms of age $a$.
$c = 0.0417\times300(a + 1)$
$c = 12.51(a + 1)$
$c = 12.51a + 12.51$

Step2: Identify slope and its meaning

The equation is in the form $y=mx+b$, where $m$ is the slope. Here, the slope is 12.51, representing the increase in child dosage (in mg) per 1 year increase in age.

Step3: Calculate newborn dosage

A newborn has age $a=0$. Substitute $a=0$ into the dosage equation.
$c = 12.51(0) + 12.51$

Answer:

(a) The slope is 12.51, representing the mg increase in child dosage per year of age.
(b) 12.51 mg