Final answer:
The current supplied by a depleting battery decreases exponentially due to the increase of the battery's internal resistance and energy dissipation from the inductor in the circuit.
Step-by-step explanation:
The student's question relates to the behavior of an electrical circuit as the power source, or battery, depletes over time. Specifically, the current supplied by a battery decreases exponentially as represented by the function i = (0.570 A)e-t/6hr. The phenomenon can be understood by examining the internal resistance of the battery, which increases as the battery is depleted. As a result of Ohm's Law, this increased internal resistance causes the current to the load resistor to decrease.
In addition, when dealing with circuits that include inductors, the energy stored within the inductor affects how the current decreases over time. The inductor stores energy and, when the circuit is disrupted, it releases this energy at a rate proportional to the square of the current, leading to an exponential decay of current, which can be visualized in graphs showing the diminishing current over time.