A city built on thick clay deposits relies entirely on groundwater pumping. In 1990, the benchmark elevation of the city center was $15.500 \text{ m}$ above mean sea level. By 2020, due to excessive groundwater extraction and subsequent clay consolidation, the same benchmark was surveyed at $13.100 \text{ m}$. Calculate the average annual rate of subsidence and project the elevation in the year 2050 if this rate remains constant.

A regional planning commission is evaluating the risk of a major landslide affecting a newly constructed highway. Geologists estimate the annual probability of a major landslide (the Hazard) at this specific location is $0.05$ ($5\%$ chance per year). The highway itself cost $50 \text{ million}$ to build, but a major landslide would completely destroy a $2 \text{ km}$ section, causing an estimated $15 \text{ million}$ in direct repair costs and economic losses (the Exposure). Because the highway is the only route to a major port, its destruction would cause severe disruption; thus, its Vulnerability factor is rated at $0.8$ ($80\%$ of the exposed value would be effectively lost). Calculate the annual Risk in dollars.

A city must choose between allocating funds to mitigate one of two different geological hazards affecting two separate neighborhoods.

Calculate the annual risk for both neighborhoods to determine which presents the higher economic priority.

A major international highway bridge is being constructed across a wide, shallow river valley whose headwaters originate on the heavily glaciated slopes of an active stratovolcano located $40 \text{ km}$ upstream.

A large, sprawling residential subdivision consisting of hundreds of single-family homes is built upon a flat, arid plain composed almost entirely of thick, expansive smectite clay deposits (montmorillonite). The region experiences severe, distinct wet and dry seasons.