[tex]m=m_0 \times (\frac{1}{2})^\frac{t}{T}[/tex]
m - the mass that remains, m₀ - the initial mass, t - time, T - the half-life
[tex]m_0=80 \ g \\
m=2.5 \ g \\
t=40 \ d \\ \\
2.5=80 \times (\frac{1}{2})^\frac{40}{T} \\
\frac{2.5}{80}=(\frac{1}{2})^\frac{40}{T} \\
\frac{1}{32}=(\frac{1}{2})^\frac{40}{T} \\
(\frac{1}{2})^5=(\frac{1}{2})^\frac{40}{T} \\
5=\frac{40}{T} \\
5T=40 \\
T=\frac{40}{5} \\
T=8[/tex]
The half-life is 8 days.
