The radioisotope cesium-137 has a half-life of 30 years. a sample decayed at the rate of 544 counts per minute in the year 1985. in what year will the decay rate be 17 counts per minute?

544 divided by 17 yields a ratio of 32. 32 is 2 to the fifth power. Therefore it will take five half-life period to decay from 544 counts per minute to 17 counts per minute. Since the half-life is given as 30 years, it will take 150 years (5 half-lives*30 years) and the goal decay rate will be achieved in the year 2135.