Ultimate BOD of a river water sample is $20$ mg/L. BOD rate constant (natural log) is $0.15 \: day^{-1}$. The respective values of BOD (in $\%$) exerted and remaining after $7$ days are:

1. $45$ and $55$
2. $55$ and $45$
3. $65$ and $35$
4. $75$ and $25$