Question

A radioactive substance decays according to the following function, where yo is the initial amount present, and y is the amount present at time t (in days).

y= y_o e^0.072t.

Find the half-life of this substance. Do not round any intermediate computations, and round your answer to the nearest tenth. days

Answer 1

`t_(1/2) \approx 9.6\,days`

Explanation:

The time constant of the radioactive constant is:

`\tau = (1)/(0.072)\,days`

`\tau = 13.889\,days`

The half-life of the substance is:

`t_(1/2) = \tau \cdot \ln 2`

`t_(1/2) = (13.889\,days)\cdot \ln 2`

`t_(1/2) \approx 9.6\,days`