Final answer:
To increase air flow back to normal with a 16x greater resistance and unchangeable airway radius, the pressure difference must be increased by a factor of 16.
Step-by-step explanation:
If you have 16x greater resistance and cannot change the airway radius, the variable you can change to increase air flow back to normal is the pressure difference (ΔP). According to the relationship Flow = ΔP / R, flow is directly proportional to the pressure difference and inversely proportional to resistance. Since resistance has increased by a factor of 16, you would need to increase the pressure difference by a factor of 16 to maintain the same flow, assuming all other factors are constant. This increase in pressure could, however, lead to strain on the heart.