$4)$ A laboratory divides a wastewater sample into several separate BOD bottles and determines the following:

after $2$ days the measured BOD is $109$ mg$/$L

after $4$ days the measured BOD is $177$ mg$/$L

after $6$ days the measured BOD is $215$ mg$/$L

after $8$ days the measured BOD is $238$ mg$/$L

after $10$ days the measured BOD is $250$ mg$/$L

Show the BOD of the sample versus time on a graph. Use the above data to find the rate constant k $($base e$)?$ Find the ultimate BOD and the BOD$5$ and show these values on the graph.