Hello, I'm sorry you haven't had a reply sooner and I hope the following is of assistance.
The distance to empty and fuel light operation are dependent on calculations from the engine management, when the lamp illuminates depends on the style of driving, the distance to empty also alters depending to the style of driving.
If on average the car is driven in an aggressive style where it uses more fuel then the lamp comes on sooner than if the car is driven in an economical style.
The distance to empty will obviously go down faster if the car is driven hard, if the car has been driven hard for a while but is then driven economically it is even possible for the distance to empty to go up rather than down.
A simple example is with 5 gallons left and the car doing 20 to the gallon the distance to empty is 100 miles, if for the next gallon of fuel used the car is doing 35 to the gallon due to a change in driving style although the car only
has 4 gallons left it's distance to empty is 140 miles, this is an extreme example but I hope demonstrates my point.
As you have just got the car it may take a few tanks of fuel to get an accurate picture depending on the previous owners driving style.
I hope this help.