Question

complete the table shown to the right for the half - life of a certain radioactive substance.
the half - life is (square) years.
(round to one decimal place as needed.)

Explanation:

Step1: Recall the formula for half - life

The formula for half - life \(T\) in the exponential decay model \(A = A_0e^{kt}\) (where \(A=\frac{A_0}{2}\) at half - life) is \(T=-\frac{\ln 2}{k}\).

Step2: Substitute the value of \(k\)

Given \(k=- 0.084\), substitute into the formula: \(T =-\frac{\ln 2}{-0.084}\).

Since \(\ln 2\approx0.6931\), then \(T=\frac{0.6931}{0.084}\).

Step3: Calculate the value

\(T=\frac{0.6931}{0.084}\approx8.2512\).

Answer:

\(8.3\)