The price of an item is initially $500. For the first 3 years the price increases by $15 each year. For the next 5 years the price decreases by $35 per year. From then on the price increases by $35 per year. Find a piecewise-defined function P that specifies the price of the item after t years have passed. Let P(t) = the price of the item in dollars after t years have passed.