What do topographic maps do and how do they do it?

The distinctive characteristic of a topographic map is the use of elevation contour lines to show the shape of the Earth's surface. Elevation contours are imaginary lines connecting points having the same elevation on the surface of the land above or below a reference surface, which is usually mean sea level. Contours make it possible to show the height and shape of mountains, the depths of the ocean bottom, and the steepness of slopes.  

USGS topographic maps also show many other kinds of geographic features including roads, railroads, rivers, streams, lakes, boundaries, place or feature names, mountains, and much more. Older maps (published before 2006) show additional features such as trails, buildings, towns, mountain elevations, and survey control points. Those will be added to more current maps over time.  

The phrase "USGS topographic map" can refer to maps with a wide range of scales, but the scale used for all modern USGS topographic maps is 1:24,000. That covers a quadrangle that measures 7.5 minutes of longitude and latitude on all sides, so these are also referred to as 7.5-minute maps, quadrangle maps, or “quad” maps (modern topographic maps for Alaska have a scale of 1:25,000 and cover a variable distance of longitude).

b - the respond is innate and varies over time.

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i believe it would be c: tons.