IgE - when does it rise?

I couldn’t find this anywhere on google (suspect my search terms were not correct terminology) so am hoping someone here will know.

When does serum IgE rise after exposure to a confirmed allergen, how long does it “last” and what is the rate of it decreasing? Is it a straight line to decrease, or a curve? Etc.. Does IgE always rise, ie. is it dose dependent? So even if a peanut allergic person had a tiny, tiny exposure would IgE definitely still rise?

Any advice appreciated.

Thanks.