You construct a topographic profile for a 1:25,000 map with no vertical exaggeration. A 100 ft change in elevation would be represented by a...

The map has a scale of 1:25,000. That is, each feature would be shown reduced by a scale of 25,000. In other words, a feature that has an actual dimension of 25,000 m, will be shown by a size of 1 m.

Here, the elevation change (to be shown on map) is 100 feet. Given the scale of the map, this feature would be reduced by a factor of 25,000 on the map. 25,000th part of 100 feet can be calculated by dividing the actual dimension by the scale. In other words,

The size of feature on the map = 100 ft/ 25,000 = 0.004 feet

A feet has 12 inches. Thus the size of the feature on the map would be 0.004 x 12 = 0.048 inches. 

Thus, the 100 feet change in elevation will be represented by a change of 0.048 inches on the profile.

Hope this helps.