Answer:
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 : 
In half an hour the trains travels 22.5 miles
I found that the given prices are $ 4 per pack of pens and $ 3 per pack of penciles.
The question is how much the bookstore spent on pens.
Then you have to multiply the number packs of pens, which is 1,528, times the price per pack pens which is $ 4.
So, the answer is: 1528 packs of pens * $ 4 / pack of pens = $6112.