Problem $1\mathrm{.}2(15$ points$)$

In the hit emotional survival story game, Life of Black Tiger, the hunter tasked to provide for himself and his family has to hunt goats for food. Calculate the time required to hunt the ${25}^{th}$ goat if the first time the hunter successfully hunted the goat took $30$ minutes, and the learning$-$curve rate for hunting is $92\mathrm{.}5\%.$