In "dr. heidegger’s experiment," what does the rose symbolize? cite evidence from the text to support your response.

The rose anticipates what happens to the guests. Dr. Heidegger first uses it to demonstrate the rejuvenating power of the elixir; and later it withers right before the same thing happens to the old guests. If you believe that the elixir is nothing more than alcohol, then the rose is a key part of the dramatic show that Heidegger puts on for his guests in order to convince them that they are in fact growing young and then old again.

In "Dr. Heidegger's Experiment" by Nathaniel Hawthorne, the rose symbolizes the passage of time and its effects. At first the rose, that has been given to the doctor by his fiancee fifty-five years ago, shows all the effects of time "...though now the green leaves and crimson petals had assumed one brownish hue..."

And his old friends are depicted "...They looked as if they had never known what youth or  pleasure was, but had been the offspring of Nature's dotage, and always the gray, decrepit,  sapless, miserable creatures, who now sat stooping round the doctor's table, without life  enough in their souls or bodies to be animated even by the prospect of growing young again ..."

Through the changes that the rose suffers, after been put in the water from the Youth Fountain, "...The crushed and dried petals stirred, and  assumed a deepening tinge of crimson, as if the flower were reviving from a deathlike  slumber; the slender stalk and twigs of foliage became green; and there was the rose of half  a century, looking as fresh as when Sylvia Ward had first given it to her love..." so we can predict what will happen to the guests.  "...Assuredly there was an almost immediate improvement in the aspect of the party...together with a sudden glow  of cheerful sunshine brightening over all their visages at once. There was a healthful  suffusion on their cheeks, instead of the ashen hue that had made them look so corpse-like..."

i don't know and i don't care .

it is the background information on the characters and setting explained at the beginning of the story. the exposition will often have information about events that happened before the story began. the exposition is often the very first part of the plot.