Question

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 200 mg.

(a) Find the slope of the graph of c. (Round your answer to two decimal places.)

(b) What is the dosage for a newborn? (Round your answer to two decimal places.)

Answer 1

a) The slope of the graph of c is 8.34.

b) The dosage for a newborn is 8.34mg.

Explanation:

A first order function in the following format

`c(a) = ba + d`

Has slope b.

The appropriate dosage c is a function of the age a.

In this problem, we have that:

`c(a) = 0.0417D(a + 1)`

Suppose the dosage for an adult is 200 mg. This means that
`D = 200`

So

`c(a) = 0.0417*200(a + 1)`

`c(a) = 8.34a + 8.34`

(a) Find the slope of the graph of c.

The slope of the graph of c is 8.34.

(b) What is the dosage for a newborn? (Round your answer to two decimal places.)

A newborn has age a = 0. So this is c(0).

`c(a) = 8.34a + 8.34`

`c(0) = 8.34*0 + 8.34 = 8.34`

The dosage for a newborn is 8.34mg.