Question

The​ half-life of radium is 1690 years. If grams are present​ now, how much will be present in ​years?.

Answer 1

Answer: ≈ 67.4 g

Step-by-step explanation:

A(t) = amount remaining in t years = A0ekt, where A0 is the initial amount and k is a constant to be determined. Since A(1690) = (1/2)A0 and A0 = 80, we have 40 = 80e1690k 1/2 = e1690k ln(1/2) = 1690k k = -0.0004 So, A(t) = 80e-0.0004t Therefore, A(430) = 80e-0.0004(430) = 80e-0.172 ≈ 67.4 g