Suppose my 10th-level wizard wakes up from a good night's rest and, using all 20 points of his Intelligence, he realizes that he needs to change his spell list a little. It's time to retire Magic Missile, and prepare Fireball instead. The other 14 spells (with a combined spell level total of, say, 35) are not changed.
That is, he is changing one of his 15 prepared spells; the new spell is a 3rd-level spell. He is not changing any of his other spells.
How long does this take?
The rules in PHB are a little vague. The description in the Spellcasting feature on PHB page 114 says (emphasis mine):
You can change your list of prepared spells when you finish a long rest. Preparing a new list of wizard spells requires time spent studying your spellbook and memorizing the incantations and gestures you must make to cast the spell: at least 1 minute per spell level for each spell on your list.
Is the wizard required to spend the full 38 minutes as if he were preparing an entirely new spell list? Or does it require only 3 minutes for the new 3rd-level spell?