On January $1\; 2004,$ two new societies, $\text{S}_1$ and $\text{S}_2$ are formed, each with $n$ members. On the first day of each subsequent month, $\text{S}_1$ adds $b$ members and $\text{S}_2$ multiplies its current number of members by a constant factor $r.$ Both societies have the same number of members on July $2,\; 2004.$ If $b=10.5n,$ what is the value of $r?$
- $2.0$
- $1.9$
- $1.8$
- $1.7$