A 100-gallon barrel, initially half-full of oil, develops a leak at the bottom. Let A(t) be the amount of oil in the barrel at 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. The mathematical model is:. (a) =kA, A(0) = 0
(b) A = ktA, A(O) = 50
(c) A tA, A(0) = 100
(d) A = két +A), A
(e) = 50 None of the above.

the mathematical model is :

Step-by-step explanation:

Given that:

Let A(t) to be the amount of oil in the barrel at time t.

However; 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.

Then,

Initially the 100 -gallon barrel is half-full of oil

So, A(0) = 100/2 = 50

The variable is now being separated as:

Taking integral of both sides; we have:

However; since A(0) = 50; Then

t = 0  ; A =50 in the above equation

Thus; the mathematical model is :

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this