Hi Emar, yes you can use both, they are interchangeable. Rise is more common in everyday speech, increase is more formulaic / mathematical.

Yes they are sometimes interchangeable like you say, and interchangeable in the situation you describe, but there are situations where either rise or increase will be correct, using the definitions you give. Increase for anything that gets bigger or grows, expands, increases weight or mass etc. And to rise/raise for going up. A thermometer's mercury will go up in the tube( rise). Although the mercury might scientifically expand/increase. we would more commonly say the temperature has risen. The mercury has risen up inside the tube.

Hi Emar. You can use either, and both are good. (Except I’d rather they decreased of course!)

Increase is appropriate to put

Actually if you follow the dictionary definitions precisely, food prices cannot increase that is grammatically incorrect. But your observations for common daily interchangeable use is correct.