Final answer:
This question pertains to mathematical calculations involving changes in elevation and slope. It focuses on understanding how altitude affects air density as well as calculating elevation differences in hiking and climbing scenarios.
Step-by-step explanation:
The question deals with changes in elevation while hiking, cave exploring, or climbing which involves calculations of distances above or below sea level and slopes based on altitude changes. For example, when an explorer is at a certain elevation and descends further, they are changing their elevation, which can be represented and calculated using numerical values - a typical mathematics problem.
To determine the elevation change when a hiker goes from one location to another on a mountain, you subtract the elevation of the second location from the first. For instance, if a hiker starts at 800m above sea level and moves to a hut at 500m above sea level, the change in elevation is 800m - 500m = 300m. When the slope between two points is needed, such as in the relationship between altitude and air density, the formula for slope (rise/run) is employed. An example provided shows the calculation of a slope which represents how air density decreases as altitude increases. Changes in elevation and slope calculations are important concepts for understanding how altitude and air density are related, as illustrated in the provided figure depicting the relationship between altitude above sea level and air density in kilograms per cubic meter.