as you go from low frequencies to higher frequencies you must create a load that is purely resistive over the test range. As you get above a certain frequency you can change from wire carried to waveguide carried RF, as the size is small enough to do it.
Waveguides are more efficient than wires in many cases and all the energy stays inside(no leaks)
That means the end of a RF waveguide load has to taper so it can appear as aperfect 50 ohm load(or whatever impedance you design it for) over the range of frequenecies.
There is usually a dielectric element inside as well that is shaped and optimized along with the heat dissipator for the job.
Aurizon did a good job of explaining the fundamentals. If you want to get into the subject more deeply, there are any number of sources which explain so-called "surge impedance" of conductor arrangements, closely enough related to your question that the exponential need will be understood. On such source is AppCad, a downloadable collection of RF information and calculating tools originated by Hewlitt-Packard. However, it is more of a calculator than an explanatory tutorial.
Incidentally, not all RF power absorbers need be exponential. Some for frequencies less than 1 GHz are made from resistive elements short enough to not be high in SWR despite lack of taper. Instruments made by Bird Engineering fall into that category.