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 $$c=0.0417 D(a+1)$$ Suppose the dosage for an adult is $200 \mathrm{mg}$. a. Find the slope. What does it represent? b. What is the dosage for a newborn?

Name: Problem 88, Chapter 1: College Algebra
Uploaded: 2021-03-04T16:36:50-08:00
Duration: 1 min 59 s
Channel: Sheryl Ezze
Description: 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=0.0417 D(a+1) Suppose the dosage for an adult is 200 mg. a. Find the slope. What does it represent? b. What is the dosage for a newborn?

   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 $$c=0.0417 D(a+1)$$ Suppose the dosage for an adult is $200 \mathrm{mg}$.
a. Find the slope. What does it represent?
b. What is the dosage for a newborn?

College Algebra

James Stewart,… 7th Edition

Chapter 1, Problem 88

Instant Answer

Solved by Expert Sheryl Ezze

03/04/2021

Step 1

0417 D(a+1)$. This gives us $c = 0.0417 \times 200 \times (a+1) = 8.34 \times (a+1)$. Show more…

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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 $$c=0.0417 D(a+1)$$ Suppose the dosage for an adult is $200 \mathrm{mg}$. a. Find the slope. What does it represent? b. What is the dosage for a newborn?

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Key Concepts

Linear Functions

A linear function, typically written as y = mx + b, models a relationship where changes in the independent variable produce proportional changes in the dependent variable. This kind of function is commonly used in practical problems to represent constant rates of change or scaling behaviors.

Slope

In a linear function, the slope (m) represents the rate of change of the dependent variable with respect to the independent variable. It indicates how much the output value changes for each one-unit increase in the input, providing a measure of sensitivity or responsiveness in the relationship.

Y-intercept

The y-intercept (b) is the value of the function when the independent variable is zero. This point often acts as a starting value or baseline in many applications, showing the output level when no effect from the input has occurred yet.

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