## Calculus 8th Edition

Published by Cengage

# Chapter 1 - Functions and Limits - 1.2 Mathematical Models: A Catalog of Essential Functions - 1.2 Exercises - Page 34: 13

#### Answer

(a) The slope is 8.34 This represents the fact that every year of a child's life the dosage they are to receive increases by 8.34 mg. (b)The dosage for a newborn is 8.34mg.

#### Work Step by Step

To find the slope of the equation, we will put the equation in slope-intercept form. That is, (1) y = mx + b The question specifies that in the equation (2) c = .0417D(a+1) c represents the child's dose of a drug in mg. D represents the adult dose of a drug. a represents the child's age. The question gives that the adult dose is 200 mg, so we take equation (1) and substitute 200 for D. (3) c = .0417(200)(a+1) Multiplying through, we get c = 8.34(a+1) Distributing 8.34, we get (4) c = 8.34a + 8.34 This is equation is now in the form y = mx + b. Thus, the slope is 8.34 This means that each year the amount that a child needs grows by 8.34. (b) To find the dosage for a new born, we plug in age a = 0. Thus, we take equation (4) and find that c = 8.34(0) + 8.34 c= 8.34. Thus, a new born should receive 8.34 mg.

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