Question

complete the table shown to the right for the half - life of a certain radioactive substance.

half - life
decay rate, k
3.3% per year = - 0.033

the half - life is (square) years.
(round to one decimal place as needed.)

Explanation:

Step1: Use the half - life formula

The formula for half - life \(T\) is \(T=\frac{\ln 2}{|k|}\). Given \(k = 0.033\).

Step2: Calculate the half - life

Substitute \(k\) into the formula: \(T=\frac{\ln 2}{0.033}\).
We know that \(\ln 2\approx0.6931\). Then \(T=\frac{0.6931}{0.033}\approx21.0\).

Answer:

\(21.0\)