Final answer:
The U.S. troop levels in Vietnam reached 500,000 during President Lyndon B. Johnson's administration as part of a significant escalation of the Vietnam War, not under Presidents Dwight D. Eisenhower, John F. Kennedy, Richard Nixon, or Gerald Ford.
Step-by-step explanation:
U.S. forces in Vietnam rose to 500,000 during the administration of President Lyndon B. Johnson. This escalation was part of President Johnson's decision to increase military involvement in Vietnam following the Gulf of Tonkin Resolution. By 1965, Johnson had committed to a large-scale deployment of troops, and the number of U.S. forces grew rapidly. The commitment to supporting South Vietnam against the North continued to escalate throughout Johnson's term, reaching over 500,000 troops.
The U.S. involvement began with military aid under President Harry Truman and continued to increase under President Dwight D. Eisenhower, who sent military advisors after the Geneva Accords. President John F. Kennedy continued the policy of supporting South Vietnam, which saw U.S. troop numbers increasing to 16,000. However, it was under Johnson that the troop numbers significantly increased to half a million. Later, President Richard Nixon pursued Vietnamization, which aimed to reduce U.S. troop involvement and eventually led to the withdrawal of U.S. forces by 1973. President Gerald Ford was in office when Saigon fell to North Vietnamese forces in 1975, but the peak troop levels occurred before his time.