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###### 58. You are deciding whether to buy a new or a two-year-old car (of the same...

58. You are deciding whether to buy a new or a two-year-old car (of the same make) based on which will have cost you less when you resell it at the end of three years. Your cost consists of two parts: the loss in value of the car and the repairs. A new car costs $20,000 and loses 12% of its value each year. Repairs are $400 the first year and increase by 18% each subsequent year. (a) For a new car, find the first three terms of the sequence dn giving the depreciation (loss of value) in dollars in year n. Give a formula for dn (b) Find the first three terms of the sequence n the repair cost in dollars for a new car in year n. Give a formula for rn (c) Find the total cost of owning a new car for three years. (d) Find the total cost of owning the two-year-old car for three years. Which should you buy?

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