Town reaching $7$ billion $(10$ points$)$

Use $lnM=nlnb$ with $b=2$ to figure out exactly $-$ via computation of doubling times $-$ how many years $($n$)$ a town, starting with $N_{1900}=100[$capita$]$ and $t_{2x}=10[yrs]$ doubling tine, would take to reach $N=7{10}^9$ people.