The key differentiation between the lysogenic and lytic cycles is that the host cell is destroyed during the lytic cycle. During the lytic cycle, the virus hijacks the host's cellular machinery to replicate itself, leading to cell lysis and release of new viral particles. In contrast, during the lysogenic cycle, the viral DNA integrates into the host's genome and replicates along with the host's DNA without causing immediate damage to the cell. Thus, the correct response is:
The host cell is destroyed during the lytic cycle.