$1\mathrm{.}6\mathrm{.}7.$ A disease is spreading through the country. Let x be the number of people infected. Let the

constant S be the number of people susceptible to infection. The infection rate $($dx$)/($dt$)$ is proportional to the

product of already infected people, x$,$ and the number of susceptible but uninfected people, S$-$x$.$

ax$(0)>0,$ that is$,$ some people are infected at time t$=0,$ what is $\backslash$lim$\_($t$->\backslash$infty $)$x$($t$).$

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