Remember, after each half-life the count rate decrease by a half. After 45 days, 3 half-lives would have passed (45 ÷ 15 = 3). This means that the count rate will have halved 3 times. The initial count rate is 200 counts per second. After 15 days it will decrease to 100 counts per second. After 30 days it will have decreased 50 counts per second. And after 45 days it will have decreased to 45 counts per second.