Data collected at a parking lot indicate that a total of $320$ cars park between $8a.m.$ and $6p.m.$

$10\%$ of these cars are parked for an average of $1hr,36\%$ for an average of $3hrs,$ and the

remaining cars are parked for an average of $8hrs.$ Determine the following: a$)$ the space$-$hours

of demand at the lot, b$)$ the number of parking bays in the parking lot if $16\%$ of the parking bays

are vacant on average $($assuming an efficiency factor of $0\mathrm{.}85),$ and c$)$ the number of additional

parking bays that will be required if the owner of the parking lot is planning an expansion of the

lot to provide adequate demand for the following $5$ years $($assuming that parking demand for all

categories will increase by $5\mathrm{.}4\%$ per year$).$