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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?
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Calculus 1 / AB
Calculus 2 / BC
Functions and Models
Mathematical Models: A Catalog of Essential Functions
Functions of Several Variables
Johns Hopkins University
Missouri State University
University of Nottingham
A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.
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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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