Final answer:
To find the time it takes for Element X to decay to 32 grams, we can set up a proportion using the half-life of Element X. Solving this proportion gives us a time of approximately 62 minutes.
Step-by-step explanation:
To find the amount of time it takes for Element X to decay to 32 grams, we can use the concept of half-life. The half-life of Element X is given as 15 minutes. This means that after 15 minutes, half of the original amount of Element X will have decayed. We can use this information to set up a proportion to find the time it takes for the element to decay to 32 grams:
(770 grams) / (32 grams) = 2(t / 15)
Solving this equation will give us the amount of time it takes for Element X to decay to 32 grams, which is approximately 62 minutes to the nearest tenth of a minute.