heart rate increases during long exercise

All the little cells are doing stuff, all the time. Chemical reactions take place, leaving by-products the cells cannot use and which may be toxic to them. One of blood's big jobs is to drop off good stuff (e.g. oxygen) that the cells need and pick up the bad stuff (e.g. carbon dioxide) the cells can't use.

When you work hard, all those cells work hard, too. Millions of chemical reactions going on, lots of little cells working at full speed. They need fresh blood constantly stopping by to drop off things they need and pick up things they don't.

So all the cells that are working hard are screaming, "FASTER! FASTER! WE NEED IT NOW!" But there is only so much blood to go around and there are so many cells requiring more.

The heart's job is to get the blood moving, so it moves (pumps) the blood faster. A faster pumping heart = a faster heart rate.

You may (or, more likely, may not) find it interesting to hear that, since there is only so much blood in there, when a bunch of cells are working harder and faster, the body shifts blood away from places that don't need it as much at that moment (like the digestive system) to places that do (like muscles) so the cells that demand more can get it.

It's a very basic explanation to a wildly involved and complicated thing and you may have already known this much, I don't know. But there you go.

Thank you so much for the information...