The first thing to look at is potassium, which would decrease because insulin facilitates intracellular shift of potassium (which is why it is used as a treatment for hyperkalemia!). This leaves only two potential answers!
The next thing I immediately noticed was that our patient's labs indicated anion gap metabolic acidosis (likely due to diabetic ketoacidosis). Administration of insulin would improve this condition, and one of the main things that would occur is correction of acidosis, so pH would increase. The other parts of the answer also make sense, as bicarbonate begins to return to normal with the increase in pH and less necessity for use in buffering, BUN decreases as the kidney damage occurring can be mostly reversed, and blood CO2 increases because there is no longer the need for respiratory compensation of the metabolic acidosis.
First recognizing her Dx just with Sx.
T1DM with confusion/sleepiness, tachycardia/tachypnea, hypotension and oliguria. All of this screams DKA with compensatory response. Confirmed by looking at her Glucose of 900.
She's given saline + insulin. Note: she would be given K+ if her K+ values were anything below 5meQ/L.
When you give insulin, you'll of course decrease glycemia, which will improve DKA. This will improve her acid/base metabolism back to normal (increase in bicarb, increase in pH). Consequently, pCO2, which was initially compensatory decreased (hyperventillation as a respiratory alkalosis). Insulin also activates Na/K+ pumps, leading to return to baseline (decrease).
Saline will help the pts hypovolemia, and consequently, her pre-renal azotemia (likely, we aren't giving Cr, but given her low volume state, we can assume its normal). Therefore, BUN will decrease, as RBC increases.