Question

The operating cost to an airline for having a fight between its west-coast and east-coast hobs changes with the price of oil. The average ticket price for a seat on one of these flights is t(f)=0.2t+10 dollars Whers f is the cotrwirg cost of one fight in dolars. When a barrel of oll is at $130, the operating cost to the airline is changing by $250 per dollar. At this oil price, what is the rate of change of ticket price with resect to the price of oil? per doliar ol price

Answer 1

The rate of change of ticket price with respect to the price of oil is 0.2 dollars per dollar of oil price.

Step-by-step explanation:

To find the rate of change of the ticket price with respect to the price of oil, we need to differentiate the ticket price function with respect to the oil price. The ticket price function is given as t(f) = 0.2t + 10 dollars, where f represents the cost of one flight in dollars. Since the cost of one flight, f, is directly related to the price of oil, we can substitute f with p, the price of oil, in the ticket price function. Therefore, the ticket price function with respect to the price of oil is t(p) = 0.2p + 10 dollars.

To find the rate of change, we differentiate the ticket price function with respect to p. The derivative of the ticket price function is dt/dp = 0.2 dollars per dollar of oil price. This means that for every 1 dollar increase in the price of oil, the ticket price increases by 0.2 dollars.