Final answer:
While electric charge is conserved in a closed circuit, the statement refers to a battery's energy, which always decreases at varying rates due to increased internal resistance as the battery depletes. Protons do not leave or enter a battery, thus, related statements about protons would be false.
Step-by-step explanation:
The question posits a scenario where a battery's charge is always decreasing over time, but it is doing so at varying rates. If we interpret 'charge' to mean the electric charge in terms of electrons, then the claim that the number of electrons leaving the battery will be equal to the number of electrons entering the battery is true in a closed circuit since electric charge is conserved.
However, if we discuss the battery's 'charge' in the context of its available energy or capacity to do work, which decreases over time, then the statement about the charge always decreasing (but at different rates) suggests the battery's ability to provide power is diminishing. This is consistent with what happens to a battery as it becomes depleted, especially considering how internal resistance can affect the rate of charge decline.
In a physical sense, protons do not enter or leave the battery since they are fixed in the atomic nuclei of the battery's material. The statement suggesting the number of protons is changing would, therefore, be false. The internal resistance in batteries, such as the rechargeable nickel-cadmium cells, increases as the battery depletes, which affects the rate at which the battery charges and discharges.