Final answer:
It will take 23.1 minutes for the sample of potassium-38 to be reduced to 25.00 mg.
Step-by-step explanation:
To determine how long it will take for a sample of potassium-38 to be reduced to 25.00 mg, we need to calculate the number of half-lives that have occurred. Each half-life is 7.7 minutes, so we can divide the initial mass by 2 for each half-life until we reach the desired mass:
200.00 mg / 2 = 100.00 mg (1 half-life)
100.00 mg / 2 = 50.00 mg (2 half-lives)
50.00 mg / 2 = 25.00 mg (3 half-lives)
Since it took 3 half-lives to reach 25.00 mg, the answer is 3 x 7.7 minutes = 23.1 minutes.