Five months into their Early Bird pilot, Starbucks found that average arrival rate at the store had plateaued at $1$ customer$/1\mathrm{.}5$ minutes. Concerned about the lack of future growth Starbucks reluctantly decided to accelerate installation plans for a service window to accommodate drive$-$thru traffic. Store Management was concerned about the effect on the brand of a customer experience that didn't involved Starbuck's classic cafe setting. Despite these concerns the installation was authorized and the affect was immediate. The average arrival rate increased $5\%$ each week with no change in service rate at $60$ customers$/$hr$.$ However, in granting the food service permits for the drive thru operation, local health officials stipulated that the store management insure the line of vehicles not extend into the heavily$-$traveled commuter parkway on which Starbucks was located. Due to the location of the hastily installed service window, the maximum allowable vehicle queue was $8$ cars. Starbuck's policy is that all store manager's have extensive experience as former baristas. The store manager is contemplating serving as an additional barista during peak hours, thus doubling the store's service rate.

$11.$ Assuming she serves as a supplemental barrista, what week after start$-$up of the drive$-$thru operations should the store manager assume the store's utilization meet or exceed $95\%?$