Question

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

k = (round to six decimal places as needed.)

Explanation:

Step1: Use the half - life formula

The formula for half - life \(T\) and decay rate \(k\) is \(T=\frac{\ln 2}{k}\). We can solve for \(k\) by re - arranging the formula: \(k = \frac{\ln 2}{T}\).

Step2: Substitute the value of \(T\)

Given \(T = 3739\) years. Substitute \(T\) into the formula: \(k=\frac{\ln 2}{3739}\).

Step3: Calculate the value

We know that \(\ln 2\approx0.693147\). Then \(k=\frac{0.693147}{3739}\approx0.000185\) (rounded to six decimal places).

Answer:

\(0.000185\)