A certain diet pill is designed to delay the administration of the active ingredient for several hours. The concentration C t (in mg/L) of the active ingredient in the bloodstream t hours after taking the pill is modeled by C t = 3 t 2 t 2 + 20 t + 51 a. Use a graphics utility to graph the function. b. What are the domain restrictions on the function? c Use the graph to approximate the maximum concentration. Round to the nearest mg/L. d. What is the limiting concentration?
A certain diet pill is designed to delay the administration of the active ingredient for several hours. The concentration C t (in mg/L) of the active ingredient in the bloodstream t hours after taking the pill is modeled by C t = 3 t 2 t 2 + 20 t + 51 a. Use a graphics utility to graph the function. b. What are the domain restrictions on the function? c Use the graph to approximate the maximum concentration. Round to the nearest mg/L. d. What is the limiting concentration?
Solution Summary: The graph of the function is shown below. The curve in the graph shows the turning point x=5
A certain diet pill is designed to delay the administration of the active ingredient for several hours. The concentration
C
t
(in mg/L) of the active ingredient in the bloodstream t hours after taking the pill is modeled by
C
t
=
3
t
2
t
2
+
20
t
+
51
a. Use a graphics utility to graph the function.
b. What are the domain restrictions on the function?
c Use the graph to approximate the maximum concentration. Round to the nearest mg/L.
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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