College tuition has risen significantly in the last tew decades. For the sake of this problem, let's assume that over the last $20$ years the cost of college, including total tuition, room, and board paid by full$-$time undergraduate students went from $$2,871$ to $$16,789$ at public institutions, a $485\%$ price increase, and from $$6,330$ to $$33,716$ at private institutions, a $433\%$ increase. Over the same time, average personal income after taxes rose from $$9,785$ to $$39,409$ per year, an increase of $302\%.$ Have these tuition increases made it more difficult for the average student to afford college tuition?