Question

8.If the adult drug dose is D (mg), pharmacists use the formula c = 0.0417D (a + 1) to determine the appropriate dose c for an older child. Suppose an adult dose is 200 mg.

Find the slope of the graph of (a) c. What does this mean?

(b) What is the dosage for the newborn baby?

Answer 1

(a) Let $a$ be an age of an child in years. Then

$$c=0.0417D\cdot a+0.0417D,\ D=const$$

Given that $D=200\ mg.$ Then the slope of the graph is

$$slope=0.0417(200)=8.34 (mg/year)$$

The slope shows that the appropriate dose c for an older child increases by $8.34$ mg if the child is one year older.

(b) Newborn baby: $a=0$

$$c(0)=0+0.0417(200)=8.34(mg)$$

The dose for newborn baby is $8.34 mg.$