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

Answer:

$t_{1/2} \approx 9.6\,days$

Step-by-step explanation:

The time constant of the radioactive constant is:

$\tau = \frac{1}{0.072}\,days$

$\tau = 13.889\,days$

The half-life of the substance is:

$t_{1/2} = \tau \cdot \ln 2$

$t_{1/2} = (13.889\,days)\cdot \ln 2$

$t_{1/2} \approx 9.6\,days$