Given:
half life of substance = 40 minutes
If the substance starts with 400g ang only 2g is left.
To find the time elapsed we have:
[tex]\text{Elapsed time = }halflife\times\frac{\log (\frac{start\text{ amount}}{end\text{ amount}})}{\log 2}[/tex]Thus, we have:
[tex]\begin{gathered} \text{Elapsed time = 40 }\times(log(\frac{400}{2})\div\log 2) \\ \\ \text{ = 40 }\times\text{ }\frac{\log 200}{\log 2} \end{gathered}[/tex]Solving further:
[tex]40\times7.64\text{ = }305.75[/tex]Therefore, the time elapsed until there is only 2g left is 305.75 minutes
ANSWER:
305.75 minutes
