Final answer:
The time for 3/4 of a sample of uranium-232 to decay can be calculated using the half-life of the isotope. In this case, it would take approximately 29.4 years for 3/4 of the sample to decay.
Step-by-step explanation:
The half-life of uranium-232 is 70 years. This means that every 70 years, half of the sample will decay. To find the time for 3/4 of a sample to decay, we need to determine how many half-lives it would take for 3/4 of the sample to remain. Since 3/4 is equal to 0.75, we can use the formula: number of half-lives = log0.5(0.75). Putting this in a calculator gives us approximately 0.415 = 0.42 half-lives. Now, we multiply this by the half-life of uranium-232 to find the time for 3/4 of the sample to decay: time = number of half-lives x half-life = 0.42 x 70 years = 29.4 years.