Answer: To create a linear model that represents the amount of fuel on the plane as a function of flight time, we need to use the given information to calculate the fuel burn rate of the airplane in gallons per hour.
Fuel burn rate = Fuel capacity ÷ Range
Fuel burn rate = 63,500 gallons ÷ 14,430 km = 4.4 gallons per km
We need to convert km to miles, as flight time is usually measured in hours and miles. We can use the conversion factor 1 km = 0.621371 miles to convert kilometers to miles.
Range in miles = Range in km ÷ 0.621371
Range in miles = 14,430 km ÷ 0.621371 = 23,594 miles
Fuel burn rate = Fuel capacity ÷ Range in miles
Fuel burn rate = 63,500 gallons ÷ 23,594 miles = 2.69 gallons per mile
Therefore, the linear model that represents the amount of fuel on the plane as a function of flight time, in hours, is:
Fuel on plane (in gallons) = Fuel capacity - Fuel burn rate x Flight time (in hours)
F(t) = 63,500 - 2.69t
where F(t) is the amount of fuel on the plane (in gallons) after flying for t hours.
Explanation: