A rate is a count window divided by its time window. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Twelve counts over three seconds

Count window 12 over 3 seconds gives rate 4 per second.

R=12÷3=4 /sR=12\div3=4\ /\mathrm{s}
Count-rate window scanThe rate changes only if the count/time ratio changes.decays=12t=3 srate=4 1/s

Twenty-four counts over six seconds

Count window 24 over 6 seconds gives rate 4 per second.

R=24÷6=4 /sR=24\div6=4\ /\mathrm{s}
Count-rate window scanThe rate changes only if the count/time ratio changes.decays=24t=6 srate=4 1/s

Thirty-six counts over nine seconds

Count window 36 over 9 seconds gives rate 4 per second.

R=36÷9=4 /sR=36\div9=4\ /\mathrm{s}
Count-rate window scanThe rate changes only if the count/time ratio changes.decays=36t=9 srate=4 1/s