Answer
$61,447.856$ slugs at time $t=100$ s.
Work Step by Step
From the graph, we find that the tangent line at $t=100$ passes through the points $(40,0)$ and $(120,10,000)$.
Note that $\frac{dv}{dt}|_{t=100}$ equals the slope of the tangent line at $t=100$. Thus, $\frac{dv}{dt}|_{t=100} = \frac{\Delta y}{\Delta x} = \frac{10,000-0}{120-40} = \frac{10,000}{80} = 125$ ft/s^2.
The mass, $M(t)$, is given as $\frac{T}{\frac{dv}{dt}}$ where $T = 7,680,982$ lb.
Thus, $M(100) = \frac{T}{\frac{dv}{dt}} = \frac{7,680,982}{125}=61,447.856$ slugs at time $t=100$ s.
