Step 1: Choose a collectible, antique, artwork or similar that is expected to appreciate selling for at least $100. You can find something at: https://www.greatestcollectibles.com/, eBay or any other site. What is the item and how much is it worth now? Include a screenshot or link. We will assume that it appreciates according to the formula, namely CCee0.5vtt where CC is the current selling price. At the beginning of the month we search ebay completed sales under most major collectibles categories. We then post the Top 3 eBay completed auctions that sold for the highest price for each category. This listing was one of the Top 3 sales for this collectibles category under Action Figures. We hope you enjoy looking at the information as much as we enjoy posting it. Please make sure you come back periodically, to see the Top collectibles that sold on eBay. every month!. #1. Top Action Figure Sold for $7,200. The item that I have chose is an action figure that is in the top 3 of the completed auctions for the action figure category and was sold for $7,200. Step 2: Your individual time period and interest rate after selling your collectible are on the next page. What is your time period and interest rate? My time period and interest rate after selling my collectible is 55 years and a 4.7% interest rate. Step 3: What would you like to use the money for in 45-55 years? I will utilize the funds to establish a business. This is the best use of the accrued funds, as I would have likely reached retirement age by this point. If the firm is successful, it helps produce a possible stable income on top of the retirement funds. Step 4: Let AA(tt) be the amount of money at the end of your time period if you sell your item after tt years. Find AA(tt) and simplify. 7200e^{.471\\sqrt(55)= 85434.29650= $85434.30 Step 5: What is the domain of AA(tt)? Remember, the domain is the relevant period for this problem. Step 6: Graph AA(tt) making sure that the entire domain that you found in Step 4 is visible and easy to see. Based on the graph, when do you think would be the best time to sell your item? How much money do you think you will have? Step 7: Use calculus to maximize AA(tt). Check your answer with your guesses in Step 5. Step 8: Will you have enough money to do what you wanted it for in Step 3 (assuming current prices, of course, not a reasonable assumption)