The function f ( x ) = 6.5 x 2 − 20.4 x + 234 x 2 + 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.
The function f ( x ) = 6.5 x 2 − 20.4 x + 234 x 2 + 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.
Solution Summary: The author explains how the pH level of the human mouth 42 minutes after eating food containing sugar is 6.0.
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.
1. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
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