Jackie has not slept for several days. when she finally dozes off, we can expect her to spend a lot of time dreaming. what process of sleep is being illustrated?

The sleep process that is being illustrated here is REM rebound.

REM rebound occurs with people who haven't slept at all for a couple of days - this means that your organism is trying to compensate for what it lost during those days of no sleep, and thus the REM activity is elevated. This means that the person will dream a lot.