A cup of coffee is taken out of a microwave oven and placed in a room. The temperature, T , in degree Fahrenheit, of the coffee after t minutes is modeled by the function T = 70 + 130 e − 0.04355 t . The graph of the function is shown in the figure. Use the graph to answer each of the following questions, a. What was the temperature of the coffee when it was first taken out of the microwave? b. What is a reasonable estimate of the temperature of the coffee after 20 minutes? Use your calculator to verify this estimate. c. What is the limit of the temperature to which the coffee will cool? What does this tell you about the temperature of the room?
A cup of coffee is taken out of a microwave oven and placed in a room. The temperature, T , in degree Fahrenheit, of the coffee after t minutes is modeled by the function T = 70 + 130 e − 0.04355 t . The graph of the function is shown in the figure. Use the graph to answer each of the following questions, a. What was the temperature of the coffee when it was first taken out of the microwave? b. What is a reasonable estimate of the temperature of the coffee after 20 minutes? Use your calculator to verify this estimate. c. What is the limit of the temperature to which the coffee will cool? What does this tell you about the temperature of the room?
Solution Summary: The author analyzes the function T=70+130e-0.04855t to determine the temperature of coffee at the time it was taken out of the microwave.
A cup of coffee is taken out of a microwave oven and placed in a room. The temperature, T, in degree Fahrenheit, of the coffee after t minutes is modeled by the function
T
=
70
+
130
e
−
0.04355
t
. The graph of the function is shown in the figure.
Use the graph to answer each of the following questions,
a. What was the temperature of the coffee when it was first taken out of the microwave?
b. What is a reasonable estimate of the temperature of the coffee after 20 minutes? Use your calculator to verify this estimate.
c. What is the limit of the temperature to which the coffee will cool? What does this tell you about the temperature of the room?
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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