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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 $. What does it represent?(b) What is the dosage for a newborn?

(a) $D=200, \operatorname{soc}=0.0417 D(a+1)=0.0417(200)(a+1)=8.34 a+8.34 .$ The slope is $8.34,$ which represents the change in $\mathrm{mg}$ of the dosage for a child for each change of 1 year in age.(b) For a newborn, $a=0,$ so $c=8.34 \mathrm{mg}$.

03:30

Jeffrey P.

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 2

Mathematical Models: A Catalog of Essential Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Harvey Mudd College

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Idaho State University

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all right, we have this equation which models the dosage see of a particular drug as a function of age A. And for this situation, we have a dosage value de of 200 milligrams, so we can substitute that into the equation. C equals 0.417 times, 200 times a plus one. And if we multiply those two numbers together we end up with 8.34 So we have C equals 8.34 times the quantity A plus one. So the slope is 8.34 And what does that mean? Let's think about the units. Slope is always a rate of change is changing. Why over change in X And in this case, that would mean change in sea. The dosage over changing a the age. What are the units on dosage and age? The dosage was measured in milligrams and the age was measured in years. So the slope is telling us the increase in the number of milligrams per year of age. So it's telling you how much to in greet increase the dose per year, increase the dose 8.34 milligrams per year Okay, That's what the slope is all about. For part B. We want to know what's the dose for a newborn baby? A newborn would have an age of zero. So if we substitute zero into the equation, we're going to get C equals 8.34 times one. And that's just 8.34 so the newborn would get 8.34 milligrams of the drug.

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