Final answer:
Applying additional thrust to increase airspeed without altering the control input would likely result in the aircraft climbing due to increased lift generated by the wings at the higher airspeed.
Step-by-step explanation:
When an aircraft is flying straight and level at a constant airspeed, the lift generated by the wings balances the weight of the aircraft. In this situation, the aircraft is flying at 15,000 feet with a 3 degree nose-up attitude and an airspeed of 180 knots. When the pilot applies additional thrust to increase the airspeed to 200 knots without applying any pressure to the stick, the nose-up attitude and the additional thrust would likely cause the aircraft to climb since more lift would be generated at a higher airspeed while the angle of attack and, consequently, the lift coefficient remain the same.