Demand for Freon 12 The demand for chlorofluorocarbon-12 (CFC-12)—the ozone-depleting refrigerant commonly known as Freon 12 63 —has been declining significantly in response to regulation and concern about the ozone layer. The graph below represents a model for the projected demand for CFC-12 as a function of time in years. 64 Time (year since 1990) a. Which is correct? Over the period [ 12 , 20 ] theinstantaneous rate of change of Q is (A) increasing. (B) decreasing. b. Which is correct? The instantaneous rate of change of demand for Freon 12 at t = 10 was (A) less than (B) greater than (C) approximately equal to the average rate of change over the interval [ 0 , 20 ] . c. Which is correct? Over the period [ 0 , 20 ] theinstantaneous rate of change Q is (A) increasing, then decreasing. (B) decreasing, then increasing. (C) always increasing. (D) always decreasing. d. According to the model, the demand for Freon 12 was decreasing most rapidly around what year? e. Roughly estimate the instantaneous rate of change of Q at t = 13 byusing a balanced difference quotient with h = 5 . Interpret the result.
Demand for Freon 12 The demand for chlorofluorocarbon-12 (CFC-12)—the ozone-depleting refrigerant commonly known as Freon 12 63 —has been declining significantly in response to regulation and concern about the ozone layer. The graph below represents a model for the projected demand for CFC-12 as a function of time in years. 64 Time (year since 1990) a. Which is correct? Over the period [ 12 , 20 ] theinstantaneous rate of change of Q is (A) increasing. (B) decreasing. b. Which is correct? The instantaneous rate of change of demand for Freon 12 at t = 10 was (A) less than (B) greater than (C) approximately equal to the average rate of change over the interval [ 0 , 20 ] . c. Which is correct? Over the period [ 0 , 20 ] theinstantaneous rate of change Q is (A) increasing, then decreasing. (B) decreasing, then increasing. (C) always increasing. (D) always decreasing. d. According to the model, the demand for Freon 12 was decreasing most rapidly around what year? e. Roughly estimate the instantaneous rate of change of Q at t = 13 byusing a balanced difference quotient with h = 5 . Interpret the result.
Solution Summary: The author explains that the instantaneous rate of change of demand of Chlorofluorocarbon-12 in time interval left[12,20right] is increasing.
Demand for Freon 12 The demand for chlorofluorocarbon-12 (CFC-12)—the ozone-depleting refrigerant commonly known as Freon 1263—has been declining significantly in response to regulation and concern about the ozone layer. The graph below represents a model for the projected demand for CFC-12 as a function of time in years.64
Time (year since 1990)
a. Which is correct? Over the period
[
12
,
20
]
theinstantaneous rate of change of Q is
(A) increasing. (B) decreasing.
b. Which is correct? The instantaneous rate of change of demand for Freon 12 at
t
=
10
was
(A) less than (B) greater than
(C) approximately equal to the average rate of change over the interval
[
0
,
20
]
.
c. Which is correct? Over the period
[
0
,
20
]
theinstantaneous rate of change Q is
(A) increasing, then decreasing.
(B) decreasing, then increasing.
(C) always increasing.
(D) always decreasing.
d. According to the model, the demand for Freon 12 was decreasing most rapidly around what year?
e. Roughly estimate the instantaneous rate of change of Q at
t
=
13
byusing a balanced difference quotient with
h
=
5
. Interpret the result.
Do the Laplace Transformation and give the answer in Partial Fractions. Also do the Inverted Laplace Transformation and explain step-by-step.
12. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.3.508.XP.
ASK YOUR TEA
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
x + 16
dx
X
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13. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.3.512.XP.
ASK YOUR TEA
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
dx
8)(2x + 1)
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14. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.3.518.XP.
Find the area of the region under the given curve from 1 to 5.
y =
x² +7
6x - x²
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DETAILS
MY NOTES
SESSCALCET2 6.3.012.
6. [-/1 Points]
Evaluate the integral.
x-4
dx
x²
- 5x + 6
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7. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.3.019.
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
x²+1
(x-6)(x-5)²
dx
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8. [-/1 Points] DETAILS
MY NOTES
SESSCALCET2 6.3.021.
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
✓
x²
4
+4
dx
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY