A clothing store has decided to move. In order to make things easier during that process, they are holding a sale at their current location and then starting fresh in their new store. They have created posters for their windows that say prices drop $5\%$ every $5$ days.

a$)$ Write the equation that models the situation.

b$)$ If a customer spots a jacket, priced at $$427\mathrm{.}49,$ what price can the customer expect in $15$ days?

c$)$ If the customer waiting for the jacket to be priced at $$100,$ how many days must they wait?