Assignment:
At a certain factory, approximately q(t) = t^2 + 50t units are manufactured during the first t hours of a production run, and the total cost of manufacturing q units is C(q) = 0.1q^2 + 10q + 400 dollars. Find the rate at which the manufacturing cost is changing with respect to time 2 hours after production commences.
Provide complete and step by step solution for the question and show calculations and use formulas.