5. What technology is seen in the painting? Why is this important to the expansion into the West?

**1. Identification of the Technology** The painting features a steam locomotive and railroad tracks. These elements clearly indicate the presence of the transcontinental railroad, a transformative piece of technology during that period. **2. Importance in the Expansion into the West** - **Facilitating Transportation:** The railroad made it possible to move large numbers of settlers and vast amounts of goods over long distances quickly. With travel times dramatically reduced (from months to weeks), the West became far more accessible. This can be conceptually represented by the relationship \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}}, \] where the reduction in time significantly increased the effective speed of travel. - **Economic Growth and Commerce:** By connecting the eastern markets with the resource-rich Western territories, the railroad promoted commerce, trade, and economic development. It enabled the efficient transportation of natural resources, agricultural products, and manufactured goods. - **Communication and Settlement:** The railroad also acted as a backbone for further technological and infrastructural developments, such as the telegraph. This dual influence helped synchronize activities from coast to coast, encouraging further settlement and coordination of government and commercial activities across the frontier. Overall, the transcontinental railroad played a critical role by making the vast expanses of the West accessible, fueling migration, spurring economic growth, and unifying the nation during a time of significant transformation.