Exercise $5-59($Algo$)$ Learning Curves $($LO $5-4)$ Fountain Precision Products $($FPP$)$ manufactures high$-$technology measurement systems. The systems are both complex and unique in the sense that only a handful are sold, usually to a single customer's specification. The last unit of model FPP$-28$X sold was the eighth produced. The labor cost for that unit was $$7,160\mathrm{.}56$ and required $128\mathrm{.}0112$ hours of labor. The second unit produced required $188\mathrm{.}0000$ hours of labor. Required: Assuming that learning has been consistent for this product, what is the rate of learning? Assuming that the hourly labor rate has remained the same, what was the labor cost to produce the fourth unit?