Final answer:
Austria-Hungary took approximately one month to respond to the assassination of Archduke Franz Ferdinand, declaring war on Serbia on July 28, 1914, after issuing an ultimatum and securing Germany's support. The complex web of European alliances rapidly converted a regional conflict into what would become World War I.
Step-by-step explanation:
After the assassination of Archduke Franz Ferdinand of Austria-Hungary on June 28, 1914, by Gavrilo Princip, a Serbian nationalist, Austria-Hungary took approximately one month to respond formally. Extensive investigations were conducted and ultimatums issued, culminating in Austria-Hungary's declaration of war on Serbia on July 28, 1914. This sequence of responses and demands further set the stage for World War I as the various alliances between European powers were activated.
Austria-Hungary felt bound by honor and strategic interest to make stringent demands on Serbia, which notably included allowing Austrian agents to conduct an investigation on Serbian soil. Serbia's partial rejection of these terms led to Austria-Hungary’s decisive action, bolstered by Germany's unconditional support, often referred to as a 'blank check.' Meanwhile, Russia prepared to defend Serbia, escalating the confrontation to a pan-European level.
The assassination and subsequent events unraveled the fragile equilibrium in Europe, leading to a general mobilization of forces and the onset of the Great War.