To determine the count rate at zero time, we can use the concept of half-life. The half-life is the time it takes for half of the radioactive substance to decay.
First, let's determine the number of half-lives that have passed during the 9 minutes.
9 minutes / 3 minutes per half-life = 3 half-lives
Since three half-lives have passed, the radioactive substance has undergone three cycles of decay. At the end of each half-life, the count rate is halved.
Therefore, after three half-lives (9 minutes), the count rate has decreased to 1/2 * 1/2 * 1/2 = 1/8 (or 0.125) of the original count rate.
If the count rate at 9 minutes is given as 200, we can determine the count rate at zero time by multiplying 200 by 8:
Count rate at zero time = 200 * 8 = 1600.
So, the count rate at zero time was 1600.