Which event most contributed to the changing troop levels shown in this graph?
the twenty-sixth amendment lowered the draft age to 18 from 21.
u. s. and north vietnamese ships exchanged fire in the gulf of tonkin.
congress expanded presidential powers to wage war under the war powers act.
communist troops launched a series of attacks during the tet offensive.

U.S. and North Vietnamese ships exchanged fire in the Gulf of Tonkin.

The answer is:

U.S. and North Vietnamese ships exchanged fire in the Gulf of Tonkin.

The Gulf of Tonkin was used by different American ships to spy on North Vietnamese radar towers, on July the submarine encountered three Soviet-made Vietnamese submarines and opened fire, this started the war on Vietnam as several shots were fired and after that the president passed the Tonin Gulf Resolution that gave him the power to declare war in southasia as he saw fit, after this more and more troops were deployed in Vietnam.

the social contract theory

b. major john c. frémont led a rebellion called the bear flag revolt.

explanation:

during the bear flag revolt, from june to july 1846, a small group of american settlers in california rebelled against the mexican government and proclaimed california an independent republic. the republic was short-lived because soon after the bear flag was raised, the u.s. military began occupying california, which went on to join the union in 1850. the bear flag became the official state flag in 1911.