The accompanying figure shows the velocity versus time curve for a rocket in outer space where the only significant force on the rocket is from its engines. It can be shown that the mass $M(t)$ (in slugs) of the rocket at time $t$ seconds satisfies the equation where $T$ is the thrust (in lb) of the rocket’s engines and $v$ is the velocity (in $ft/s$) of the rocket. The thrust of the first stage of a Saturn V rocket is $T = 7744393$ lb. Use this value of $T$ and the line segment in the figure to estimate the mass of the rocket at time $t = 100$.

(click to enlarge)

$M(100)=$