Final answer:
Black holes obtain their 'food' from the surrounding galaxy, primarily through interstellar matter from within the galaxy, as well as from the accretion of nearby material and the influx of matter due to galactic collisions.
Step-by-step explanation:
Black holes 'feed' on material such as gas, dust, and even stars from their surrounding galaxy. A primary source of a black hole's 'food' is the interstellar matter within the host galaxy itself, which can include the remnants of stars that have died and released material back into space. Over time, this can lead to a decrease in quasars' number and luminosity as the available matter is consumed or converted into stars.
Additionally, black holes can grow larger through the accretion of matter that gets too close to their event horizon, forming an accretion disk that sometimes flings some material outward. Furthermore, when galaxies collide, the tremendous forces can cause massive amounts of dust and gas to fall into their central black holes, potentially fueling a quasar. Such galactic collisions are another significant source of material for black holes to 'feed' on.