At the band’s peak of popularity, a signed Black Diamond poster sold for $$500$. Three years later, the band was almost forgotten, and the poster was worth only $$10$.

1. What is the annual rate of depreciation for the poster?

   Hint (a):

   An exponential function is always of the form $y=ab^x$.

2. Write a function that will allow you to calculate how much the poster is worth after $x$ years. State the meaning of each part of the equation in the context of the problem.