$1(20$ points$).85$ percent is believed to be the learning rate to produce a new product. Suppose that the time to produce the ${15}^{th}$ unit is $9$ hours and $30$ minutes.

$($a$)(10$ pts$)$ What is the time to produce the first unit?

$($A$)15\mathrm{.}05$ hours

$($B$)15\mathrm{.}89$ hours

$($C$)16\mathrm{.}65$ hours

$($D$)17\mathrm{.}95$ hours

$($b$)(10$ pts$)$ What is the time to produce the ${20}^{th}$ unit?

$($A$)5\mathrm{.}45$ hours

$($B$)6\mathrm{.}65$ hours

$($C$),7\mathrm{.}70$ hours

$($D$),8\mathrm{.}85$ hours