Question

A certain radioactive material, radium-226, decomposes according to the formula A = Aoe^kt where A is the remaining mass after decomposition, Ao is the original mass, t is the time in years and k is a constant. A radioactive substance is often described in terms of its half-life, which is the time required for half the material to decompose. Given that after 500 years, a sample of radium-226v has decayed to 80.4% of its original mass, find the value of k.​

Answer 1

k = -0.0004463

Explanation:

A = Aoe^kt

"a sample of radium-226v has decayed to 80.4% of its original mass"

We can state from this that A = 0.804Ao

(0.80)Ao = Aoe^kt

0.80 = e^kt

t is 500 years

0.80 = e^k(500)

k = -0.0004463