Answered: y 7.0 6.5 6.0 5.5 5.0 6.5x - 20.4x +…

y 7.0 6.5 6.0 5.5 5.0 6.5x - 20.4x + 234 %3D 4.5 x? + 36 4.0 0 6 12 18 24 30 36 42 48 54 60 66 Number of Minutes after Eating Food Containing Sugar pH Level of the Human Mouth 10554

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

Question

The function f(x) =(6.5x² - 20.4x + 234)/(x² + 36)models the pH level, f(x), of the human mouth x minutes after a person eats food containing sugar. The graph of this function is shown in the figure.

a. Use the graph to obtain a reasonable estimate, to the nearest tenth, of the pH level of the human mouth 42 minutes after a person eats food containing sugar.
b. After eating sugar, when is the pH level the lowest? Use the function’s equation to determine the pH level, to the nearest tenth, at this time.
c. According to the graph, what is the normal pH level of the human mouth?
d. What is the equation of the horizontal asymptote associated with this function? Describe what this means in terms of the mouth’s pH level over time.
e. Use the graph to describe what happens to the pH level during the first hour.

y
7.0
6.5
6.0
5.5
5.0
6.5x -
20.4x + 234
%3D
4.5
x? + 36
4.0
0 6 12 18 24 30 36 42 48 54 60 66
Number of Minutes after
Eating Food Containing Sugar
pH Level of the
Human Mouth
10554

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