The 1980s Saw a Trend Toward Old-Fashioned Punitive Deterrence as Opposed

Short Answer

The 1980s saw a trend toward old-fashioned punitive deterrence as opposed to the more liberal penal policies and community-based corrections popular in the 1960s and early 1970s. As a result, prisons became more crowded, and the gap between the number of people in prison and the prison capacity widened. The number of prisoners (in thousands) in federal and state prisons is approximated by the function
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where t is measured in years, with t = 0 corresponding to 1983. The number of inmates for which prisons were designed is given by
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where C(t) is measured in thousands and t has the same meaning as before. Find an expression that shows the gap between the number of prisoners and the number of inmates for which the prisons were designed at any time t.