Question

Actinium-227 is a radioactive substance that decays according to the following function, where yo is the initial amount present, and y' is the amount present at

timer (in years).
-0.0321
yayoe
Find the half-life of Actinium-227. Do not round any intermediate computations, and round your answer to the nearest tenth.
X

Answer 1

The half-life of Actinium-227 is approximately 18.4 years.

Step-by-step explanation:

The half-life of Actinium-227 can be found using the decay function provided.

The decay function is given by the equation y' = -0.0321y.

The half-life is the time it takes for half of the initial amount to decay, so when y' = -0.0321y, we can set y' = -0.5yo (where yo is the initial amount) and solve for t.

-0.5yo = -0.0321yo

0.468 = e^(-0.0321t)

t = ln(0.468) / (-0.0321)

= 18.4 years

Therefore, the half-life of Actinium-227 is approximately 18.4 years.