A certain radioactive substance has a half of 30 minutes. If the count rate was observed to be 300 after 90 minutes, determine its count rate at the beginning.
The count rate at the beginning would be 900. This is because the half-life of the substance is 30 minutes, so after 90 minutes, the count rate would have decreased by a factor of 3 (half of the original count rate three times). Therefore, the original count rate would be 3 times the current count rate, or 900.
x at start
1/2 x at 30 min
1/4 x at 60 min
1/8 x at 90 min
x = 8 * 300