Problem $3.3(25$ Points$)$ Your boss is the director of reporting for the Athens County Construction Agency $($ACCA$).$ It has been his job to track the cost of construction in Athens County. Twentyfive years ago, he created the ACCA Cost Index to track those costs. Costs during the first year of the index were $$14$ per square foot of constructed space $($the index value was set at $200$ for that first year$).$ This year a survey of contractors revealed that costs were $$70$ per square foot.

$($a$)$ What index number will your boss publish in his report for this year?

$($b$)$ If the index value was $500$ last year, what was the cost per square foot last year?