Final answer:
To determine the amount of potassium-42 left after a certain time, we can use the concept of radioactive decay and the half-life of potassium-42. After 74.4 hours, approximately 11.72 g of a 745 g sample of potassium-42 will be left.
Step-by-step explanation:
To determine how much of a 745 g sample of potassium-42 will be left after 74.4 hours, we can use the concept of radioactive decay and the half-life of potassium-42. The half-life of potassium-42 is 12.4 hours, which means that in 12.4 hours, half of the sample will decay.
Since 74.4 hours is 6 times the half-life, we can calculate the remaining amount by continuously dividing the initial sample amount by 2. After the first 12.4 hours, half of the sample will decay, leaving us with 745 g / 2 = 372.5 g. After the second 12.4 hours, another half will decay, leaving us with 372.5 g / 2 = 186.25 g. This process will continue for a total of 6 times, resulting in an answer of approximately 11.72 g.