I believe I have the mathematical model correct. My main concern is part d. I am unsure of how to even approach this. Do I need to first calculate how much oil is cleaned after 25 days with my math model from part a? Then, how do I include the 100 barrels part?
I cannot use formulas only discrete dynamical systems. 
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So do I interpret it correctly that your model is, that on the $n$:th day there is $$ f(n) = -0.1 n + 4000 $$ barrels of oil? I don't think this is exactly correct ... The statement says "crews are able to remove about $10~%$ of the oil in the water each day". So in the beginning, there is $4000$ barrels, on the next day there is $0.9 \times 4000$, on the day after that there's $0.9 \times 0.9 \times 4000$ ... Do you agree? – Matti P. Jan 27 '20 at 07:01
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1You went wrong right at the start. The oil is leaking continuously 4000 per day. The cleanup removes 10% of the total not so far removed. You seem to be working on the basis that the spillage is not continuing, so there is only a total of 4000 to remove. – almagest Jan 27 '20 at 07:03
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I agree with @almagest. The model does not take into account that there is an additional spill of $4000$ barrels of oil every day. The current model only considers [the accuracy of which needs to be re-evaluated] one oil spill and predicts the fraction of this remaining after $n$ days. – an4s Jan 27 '20 at 07:13