When research on exercise is done on healthy, young adults can the results be applied to older adults with conditions like arthritis or disc disease?

Good question. Strictly speaking, the answer is "no." But in the big picture, scientists have to start somewhere. Using normal, healthy, young adults who have no history of injury or illness gives an idea of what is "normal." The norm can be used to compare results to all others.

In order to use this information from normal adults to plan exercise programs, further studies are done. The researchers will need to repeat the same exercise program on different age groups. The response of different joints will also be studied. Then finally, groups with various diseases, illnesses, or injuries form the subjects of final studies.

Often useful information is collected studying a normal adult, good information that transfers well to other "less well" individuals.