An engineer is testing a prototype electric water pump designed for off-grid irrigation. During a trial run, the pump operates continuously for 450 s450\text{ s}450 s. It delivers a constant useful mechanical power output of 16 W16\text{ W}16 W and has an efficiency of 32%32\%32%.
Calculate the total useful energy output of the pump during this trial.
State the equation linking efficiency, useful energy output, and total energy input.
Calculate the total energy input to the pump during this period.