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