Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Section 6.1 - Rational Expressions and Functions; Multiplying and Dividing - Exercise Set - Page 416: 112

Answer

Decreases to a minimum of $4.8$, then increases to $6.2$

Work Step by Step

We are given the function: $$f(x)=\dfrac{6.5x^2-20.4x+234}{x^2+36}.\tag1$$ Graph the function $f$. We notice that right after a person eats food containing sugar the pH level decreases to a minimum of $4.8$ in about $6$ minutes. Then the level of pH starts to increase and after one hour it reaches the value of $$f(60)=\dfrac{6.5(60^2)-20.4(60)+234}{60^2+36}\approx 6.2$$. The increase continues over time and gets closer and closer to $6.5$.
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