Final answer:
The amount of strontium-90 remaining after 152.4 years can be calculated using the formula A(t) = A₀ * (1/2)^(t/h), where A₀ is the initial amount of strontium-90, t is the elapsed time, and h is the half-life of strontium-90. By substituting the given values into the formula, we find that approximately 9 mg of strontium-90 will remain after 152.4 years.
Step-by-step explanation:
To determine the amount of strontium-90 remaining after a certain period of time, we can use the formula: A(t) = A₀ * (1/2)^(t/h) Where: A(t) is the amount of strontium-90 remaining after time t A₀ is the initial amount of strontium-90 t is the elapsed time h is the half-life of strontium-90 Given that the half-life of strontium-90 is 38.1 years.
the initial amount of strontium-90 is 36 mg, and the elapsed time is 152.4 years, we can substitute these values into the formula: A(152.4) = 36 * (1/2)^(152.4/38.1) Calculating this equation gives us: A(152.4) ≈ 9 mg. Therefore, the amount of strontium-90 remaining after 152.4 years is approximately 9 mg.