The half-life of a compound is the time needed to the mass to reduce to half of its initial value. If x is the time in years, x₀ is the half-life or the compound, m₀ the initial mass, m the mass after x years, we can use the following formula:
[tex]m=\frac{m_0}{2^{\frac{x}{x_0}}}[/tex]For m = 22 grams, x₀ = 30 years, and x = 11 years, we are looking for the value of m₀. From the first relation, we can isolate m₀ and substitute the values:
[tex]\begin{gathered} m_0=m\times2^{\frac{x}{x_0}} \\ m_0=22\times2^{\frac{11}{30}}=22\times2^{1.289}\cong28.37grams \end{gathered}[/tex]From the present solution, we conclude the answer is c. 28.37 grams.
