Final answer:
ATP stores during prolonged exercise are replenished by aerobic respiration, which is a highly efficient process occurring in the mitochondria that uses oxygen to break down glucose, providing a sustained supply of energy.
Step-by-step explanation:
During a prolonged bout of continuous exercise, longer than 30 minutes, ATP stores are replenished by aerobic respiration. This process takes place in the mitochondria and involves the breakdown of glucose in the presence of oxygen to produce ATP, which is then used for muscle contraction and various other cellular processes. While the muscle can generate ATP without oxygen through glycolysis, producing lactic acid as a by-product, this is not sustainable for long periods. It is through aerobic respiration that muscles obtain the necessary ATP to sustain prolonged activity. The glucose used in this process can come from blood glucose or by metabolizing glycogen that is stored in the muscle. Moreover, aerobic respiration is much more efficient than glycolysis, being able to support the energy needs of a working muscle much longer.