CALCULUS:GRAPHICAL,NUMERICAL,..-PACKAGE
5th Edition
ISBN: 9780133320381
Author: Finney
Publisher: SAVVAS L
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Fossil-fuel emissions The amount of carbon in the
atmosphere has been estimated to have increased at a
rate of about 3.09% per year since 1850. This increase
is due to carbon emissions from fossil-fuel burning and
can be modeled by the differential equation
dE
= 0.0309E
dt
where t is the number of years since 1850 and E is
fossil-fuel emissions in millions of metric tons per year.
(a) Solve this differential equation, and find a particu-
lar solution that satisfies E(0)
(b) The graph shows actual CO emissions since 1815.
Graph your solution and compare it with the graph
below for the years since 1850.
85.53.
Global CO, emissions
8000
6000
4000
2000
1815
1880
1945
2010
Year
Source: New York Times, September 14, 2004. Copyright 2004
The New York Times Co. Reprinted with permission.
Million metric tons of carbon
Use Linear Differential Equation
In differential equations, solve the following:
Knowledge Booster
Similar questions
- Subject: calculusarrow_forwardThe rate of change of y with respect to x is proportional to y². (a) Write a differential equation for the statement. (Use k for the constant of proportionality.) x=k-y² dy dx (b) Match the differential equation with a possible slope field. Verify your result by using a graphing utility to graph a slope field for the differential equation. **** I x Need Help? Read It /**** 17 **** ** 771 11arrow_forwardTutorial Exercise Determine whether the function is a solution of the differential equation y(4) – 81y = 0. y = 5e3x – 2 sin 3x Step 1 To verify the solution of the differential equation, first find the derivative derivative of the given function y = 5e3x – 2 sin 3x. Step 2 Differentiate the given function y four four times, as the verification needs to be done for y(4) in the left side of the differential equation. Step 3 Now differentiate the given function y = 5e3x - 2 sin 3x, to obtain the first derivative. y' = 5e (3) – 2 cos(3x)(3) y' 3 1 X cos 3x = 5 X e Submit Skip (you cannot come back)arrow_forward
- DIFFERENTIAL EQUATION: A year-end party is being held in a room that contains 30 m3 of air which is originally free of carbon monoxide. Beginning at time t = 0, several people start smoking cigarettes. Smoke containing 6 percent carbon monoxide is introduced into the room at the rate of 0.008 m3/minute, and the well-circulated mixture leaves at the rate of 0.016 m3/minute through a medium-sized open window. A sustained carbon monoxide concentrations above 200 ppm (parts per million) may cause harm. Understanding this situation, An person decides to leave this party. How much time is left, after the start of the party, that will still allow the person to safely exit the party?arrow_forwardRaviarrow_forwardcup of coffee is made with boiling water at a temperature of 100°C in a room with ambient temperature 20°C. After 4 monites the coffee has cooled to 90°C a. What is the equation T(t) for the temperature of this coffee? b. What is the temperature of coffee after 8 minutes? c. Does the coffee cool more the first 4 minutes or the second 4 minutes? Why does this make sense in term of the differential equation?arrow_forward
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