= Solution
For a spherical <mass> distribution, the <shell theorem> says the circular gravitational acceleration is $GM(<R)/R^2$. Balancing it against the centripetal acceleration $V_c^2/R$ gives
$$
M(<R)=\frac{RV_c^2(R)}G.
$$
At $R=16\ \mathrm{kpc}=4r_0$, the <galaxy rotation curve> gives $V_c=200(1-e^{-4})=196.337\ \mathrm{km\,s^{-1}}$. With $R=4.93708\times10^{20}\ \mathrm m$,
$$
\boxed{M(<16\ \mathrm{kpc})=2.8515\times10^{41}\ \mathrm{kg}=1.4340\times10^{11}M_\odot.}
$$
This is the total dynamically inferred enclosed <mass>, including any <dark matter>; the <galaxy rotation curve> alone does not separate its components.
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