What will happen is that when you stop exercising your pulse rate will just steadily go down to your usual 'relaxed' rate. That's how the system (your body's cardiovascular system, that is) works. When you begin exercising your heart beats more times per minute to pump more blood round, -to power your muscles. The harder you work out, the more blood is pumped, and vice versa. When you slow down so does your heart. At the opposite end, when you go to sleep, your pulse rate gradually falls .. So if your usual daytime 'rest state' pulse is about 75 bpm, you will find that it will drop down to as low as even perhaps 45-55 bpm when you're in deep sleep.. Contrary to what you'll read in books (and on Answers especially) , there is no truly "REST" condition... Your pulse (and blood pressures) can vary from deep sleep to high stress exercise levels. It's a continuous scale.