Answer:
[tex]\frac{\mathrm{d} A}{\mathrm{d} t}=ktA\,,\,A(0)=50[/tex]
Step-by-step explanation:
A(t) denotes the amount of oil in the barrel at time t.
As 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,
[tex]\frac{\mathrm{d} A}{\mathrm{d} t}=ktA[/tex]
Here, k is a constant term.
As a 100-gallon barrel initially contains half-full of oil,
[tex]A(0)=50[/tex]
