In a certain manual operation, the first work unit required $7\mathrm{.}54$ min to

complete and the learning rate is known to be $86\%$ in the Wright model.

Using this learning curve model, determine:

$($a$)$ The average cumulative times to produce the second unit. $(3$ marks$)$

$($b$)$ The average cumulative times to produce the $10$th unit. $(2$ marks$)$

$($c$)$ The average cumulative times to produce the $100$th unit. $(2$ marks$)$

$($d$)$ The total cumulative time for the $100$ units and the unit time for the $100$th

unit. $(3$ marks$)$