The aircraft weighed 350,000 kg at takeoff and is losing weight as the flight goes on, so we need to subtract the fuel burn (in kg/h) multiplied by the time:
Answer: `w(t) = 350,000 - 13,000t`
For example, after flying for 6 hours, the aircraft would weigh:
`w(6) = 350,000 − 13,000 × 6 = 272,000\ "kg"`
Note: Like many mathematical models, this is a very simplified version of the real situation. A plane burns fuel at different rates during taxi (on the ground, where the engines run inefficiently), take-off (which is the time of maximum fuel burn), climb, cruise at the beginning (when it is heavy), cruise towards the end (when it is lighter), and descent (when it uses very little fuel).
Factoid: It costs upwards of US`$200,000` to fill the tanks of a 747.