Answer:
23.90 years
Step-by-step explanation:
To find the half-life of a radioactive substance, we can use the formula:
[tex]\boxed{\begin{minipage}{10 cm}\underline{Half-life formula}\\\\$ t_{1/2} =\dfrac{\ln 2}{k}$\\\\where:\\\\ \phantom{ww}$\bullet$ $t_{1/2}$ is the half-life. \\ \phantom{ww}$\bullet$ $k$ is the decay constant (percentage decay rate per year)\\ \end{minipage}}[/tex]
In this case, the decay constant is 2.9% or 0.029 (expressed as a decimal). Therefore, substitute k = 0.029 into the formula:
[tex]t_{1/2} =\dfrac{\ln 2}{0.029}[/tex]
[tex]t_{1/2} =23.9016269...[/tex]
[tex]t_{1/2} =23.90\; \sf years\; (2\;d.p.)[/tex]
Therefore, the half-life of the radioactive substance, rounded to 2 decimal places, is approximately 23.90 years.
