battery/mileage puzzle

Here's a puzzler. I have a 2000 Beetle TDi. Until about 2 months ago,
I averaged 40 mpg in the city. Two months ago, my mileage dropped
progressively to 38 mpg, then 35 mpg. A month ago the battery died.

I put the new battery in, and for the first 2 tankfuls, I am back at
between 40 and 41 mpg.

My driving pattern and habits haven't changed (95% city), nor have I
changed the station where I fill diesel. I haven't done any oil changes,
changed the tire pressure, or performed any other work on the car.

So why has my mileage returned to what it used to be after I changed
the battery?

AC
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Email: echo 36434455860060025978157675027927670979097959886449 930P | dc

Dying battery causes alternator to work harder, thereby causing motor
to work harder?