Cowling's Rule is a method for calculating pediatric drug dosages. If a denotes the adult dosage (in milligrams) and if t is the child's age (in years), then the child's dosage is given by
D(t) = (t + 1/24)a
(a) Show that D is a linear function of t.
Hint: Think of D(t) as having the form
D(t) = mt + b.
What are the slope m and the y-intercept b?
m = ______
b = ______
To show that D is a linear function of t, we need to rewrite the formula for D(t) in the form D(t) = mt + b, where m is the slope and b is the y-intercept.
Using Cowling's Rule formula: D(t) = (t + 1/24)a
We can see that the coefficient of t is 1, and since the constant term is 1/24, we can rewrite the formula as:
D(t) = (1/24)t + a
Comparing this with the equation of a line, we can identify that m, the slope, is 1/24 and b, the y-intercept, is a.
Therefore:
m = 1/24
b = a