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Calculus and Beyond Homework Help
(Differential equation) Finding an exponential equation
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[QUOTE="namegoeshere, post: 4287294, member: 464261"] [h2]Homework Statement [/h2] A 44 gallon barrel of oil develops a leak at the bottom. Let [itex]A(t)[/itex] be the amount of oil in the barrel at a given time [itex]t[/itex]. Suppose that the amount of oil is decreasing at a rate proportional to the product of the time elapsed and the amount of oil present in the barrel. a. Give the mathematical model for A b. Find the general solution of the differential equation c. Find the particular solution for the initial condition [h2]Homework Equations[/h2] [h2]The Attempt at a Solution[/h2] a. [CENTER][itex]\frac{\partial{A}}{\partial{t}} = -Akt[/itex][/CENTER] b. [CENTER][itex]\int{\frac{1}{A}\,dA} = \int{-kt\,dt}[/itex] [itex]\ln{A}=\frac{kt^2}{2}+C[/itex] [itex]A(t)=Ce^\frac{-kt^2}{2}[/itex][/CENTER] c. [CENTER][itex]44=Ce^0[/itex] [itex]A(t)=44e^\frac{-kt^2}{2}[/itex][/CENTER] Is this correct? I'm not sure if I came up with the right [itex]\frac{\partial{A}}{\partial{t}}[/itex]. [/QUOTE]
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Calculus and Beyond Homework Help
(Differential equation) Finding an exponential equation
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