The 1980s saw a trend toward old-fashioned punitive deterrence in contrast to the more liberal penal policies and community-based corrections that were 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 prison capacity widened. based on figures from a certain government agency, the number of prisoners (in thousands) in federal and state prisons is approximately 3.9t2 + 26.8t + 436.3 (0 ≤ t ≤ 10) and the number of inmates (in thousands) for which prisons were designed is given by 24.2t + 363 (0 ≤ t ≤ 10) where t is measured in years, and t = 0 corresponds to 1984. find an expression giving the gap between the number of prisoners and the number for which the prisons were designed at any time t.