The companion to the e splitting. Under the stress of the present tense, an o in the root may split into ue. You already knew one example: puedo is a split o.
e → ie · o → ue
It is the accent on the penultimate syllable, one of the fundamental elements of the present tense, that makes the vowel vulnerable to splitting in the first place.
Duerme · Duermen · Muestra · Muestran · Empieza · Empiezan · Empiezas · ¿Cuándo empiezas?
Asked for he starts, the student offers "empieze". The fix is always the same.
empezar → empeza → empieza. Run the process in that order and it comes out right.
The same phenomenon is visible in words that crossed over, which makes it much easier to trust.
Población is an exception to the -ción pattern: not "populación". You can see pob- splitting into pue- in pueblo.
Mortgage literally means "death pact": mort- is the Latin root for death and -gage means pact.
At school you are told a noun is a thing or an object. La muerte (the death) is not an object, but it is a noun, because you can put the in front of it.
The adjective goes plural too: muertos, muertas.
Do not assume a word is a verb just because it looks like one. Any version of a verb, the "to" form or another, might also be a noun. Whatever you can put a or the in front of is a noun.
Same with muestra: it is he/she/it shows, but una muestra is a sample.
The z in empezar sounds /th/ in most of Spain: empe/th/ar.
To fall asleep is to sleep myself: me duermo, as against plain duermo for I sleep.
Me duermo · Lo encuentro · Muestra needs no rolled r: it is a single r.