jdl,
Stuart doesn't understand yet! My flawed logic would tell me that the 'empty' battery would 'fill' quite fast at first, tapering to very slow as it reached 'full'.
If you watch the ammeter on a battery charger, or even your ammeter equipped truck, the charge rate goes from high to low as the battery is 'filled', or charged. As the potential in the battery reaches the output capacity of the charging device, the rate of charge slows. Maybe the generator/voltage regulator deal the Jerry explained works differently, I don't know.
Stuart