Given
half life in 6m
Initial 680g
Procedure
[tex]y=a(0.5)^{\frac{t}{h}}[/tex]
This is the model we can use to calculate the decay. But we must recognize the values of a and of h
The value of a corresponds to the initial value of the population, which in our case is 680g.
While the value of h will be the number of minutes it takes to reach its half-life. Therefore:
[tex]y=680\cdot0.5^{\frac{t}{6}}[/tex]
With this formula, we can now proceed:
[tex]\begin{gathered} 276=680\cdot0.5^{\frac{t}{6}} \\ \frac{276}{680}=0.5^{\frac{t}{6}} \\ \ln \frac{276}{680}=\ln 0.5^{\frac{t}{6}}^{} \\ \frac{t}{6}\ln 0.5=\ln \frac{276}{680} \\ t=\frac{6\ln \frac{276}{280}}{\ln 0.5} \\ t=7.8\text{ min} \end{gathered}[/tex]
