Answer:
The half-life of this substance would be 8 day
Step-by-step explanation:
Given equation that shows the amount of the substance after t days,
[tex] y = ne^{-0.0856t}[/tex]
Where,
n = initial quantity of the substance
If y = n/2,
[tex]\frac{n}{2}=ne^{-0.0856t}[/tex]
[tex]\frac{1}{2}=e^{-0.0856t}[/tex]
Taking ln both sides,
[tex]\ln (\frac{1}{2}) = -0.0856t[/tex]
[tex]-0.69315 = -0.0856t[/tex]
[tex]\implies t =\frac{-0.69315}{-0.0856}=8.0975\approx 8[/tex]
Hence, the half-life of this substance would be 8 days.