How does the allowable power density for RF safety change if duty cycle changes from 100 percent to 50 percent?
Why RF exposure limits are based on power density averaged over a fixed evaluation period (6 minutes for controlled, 30 minutes for uncontrolled exposure). If your transmitter is only on half the time, the average exposure is half the peak value, so the peak power density you are allowed to produce can be twice as large and still meet the same average limit. Cutting duty cycle in half therefore doubles the allowable power density.
Watch out The idea that it decreases by 50 percent has the relationship backwards: less transmitting time means less average exposure, which relaxes rather than tightens the allowed peak level. Duty cycle adjustment is explicitly permitted in FCC exposure evaluations, so 'no adjustment allowed' is also wrong.
Half the on-time, twice the allowed power density. Duty cycle and allowable density move in opposite directions.