Exponential Equations 25

Question

The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain after 1000 years?

___   mg

Answer 1

A = 200(0.5)^1000/1590

A = 200(0.5)^0.628930817

A ≈ 200(0.646 655474)

A ≈ 129.331095

Answer 2

Let A(t) = amount remaining after t years

A(t) = 200e^-kt, for some constant, k.

Since A(1590) = 100, we have 100 = 200e^-1590k.

So, e^-1590k = 0.5

-1590k = ln(0.5) So, k = 0.0004359

A(t) = 200e^-0.0004359t

A(1000) = 200e^-0.4359 ≈ 129.3 mg