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namegoeshere
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Homework Statement
A 44 gallon barrel of oil develops a leak at the bottom. Let A(t) be the amount of oil in the barrel at a given time t. 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
Homework Equations
The Attempt at a Solution
a.
\frac{\partial{A}}{\partial{t}} = -Akt
b. \int{\frac{1}{A}\,dA} = \int{-kt\,dt}
\ln{A}=\frac{kt^2}{2}+C
A(t)=Ce^\frac{-kt^2}{2}
c. \ln{A}=\frac{kt^2}{2}+C
A(t)=Ce^\frac{-kt^2}{2}
44=Ce^0
A(t)=44e^\frac{-kt^2}{2}
A(t)=44e^\frac{-kt^2}{2}
Is this correct? I'm not sure if I came up with the right \frac{\partial{A}}{\partial{t}}.
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