Question

The half-life is blank years. Round to one decimal place as needed

Answer 1

The formula to apply is

`\begin{gathered} A=A_oe^(-\lambda t) \\ Where\text{ A = amount of substance remaining = 0.5, after half decayed} \\ A_o=1 \\ \lambda=0.051 \\ t=\text{ time in years } \end{gathered}`

Putting in the values into the formula, we have

`\begin{gathered} 0.5=1* e^(-0.051t) \\ 0.5=e^(-0.051t) \\ Taking\text{ ln of both sides, we have} \\ ln0.5=-0.05t \\ t=(ln0.5)/(-0.051) \\ t=13.59112 \end{gathered}`

Hence the answer is 13.6 years to 1 d.p