4. (2 pts) \( f(p) \) dollars gives the operating cost to an airline for a flight from City A to City B when oil is \( p \) dollars per barrel. Assume: Oil is sold for \( \$ 120 \) per barrel at the moment in question. \[ \left.\frac{d f}{d p}\right|_{p=120}=200 \] \( T(f)=0.03 f+10 \) dollars gives the ticket price for that flight from City A to City B when the operating cost is \( f \) dollars. At the moment in question, find and write a sentence of interpretation for \( \frac{d T}{d p} \).

At the moment in question, \( \frac{d T}{d p} \) represents the rate of change of the ticket price \( T \) with respect to the price of oil \( p \). Given that \( \frac{d T}{d f} = 0.03 \) and \( \frac{d f}{d p} = 200 \), we can use the chain rule to find \( \frac{d T}{d p} = \frac{d T}{d f} \cdot \frac{d f}{d p} = 0.03 \cdot 200 = 6 \). This means that for every dollar increase in the oil price per barrel, the ticket price will rise by approximately $6, indicating a direct correlation between oil prices and ticket costs. In essence, as oil becomes more expensive, passengers will see higher fares as airlines adjust to maintain their operating margins.