Answer: To determine how much of the radioactive europium will be left after 75 years, we can use the half-life formula:
Amount remaining = Initial amount * (1/2)^(time elapsed / half-life)
Given that the half-life of the radioactive europium is 15 years and the initial amount is 90,624 grams, we can substitute these values into the formula:
Amount remaining = 90,624 * (1/2)^(75 / 15)
Calculating the exponent first:
(75 / 15) = 5
Substituting this back into the formula:
Amount remaining = 90,624 * (1/2)^5
Simplifying the exponent:
(1/2)^5 = 1/32
Substituting this back into the formula:
Amount remaining = 90,624 * 1/32
Simplifying the calculation:
Amount remaining = 2,832 grams
Therefore, after 75 years, there will be approximately 2,832 grams of the radioactive europium left.