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Math Help - Spending Question and functions.

  1. #1
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    Spending Question and functions.

    Hello everyone, I've been trying to solve this question for quite some time but I cannot do it. If anyone can show me how it would be greatly appreciated.

    The cost of a refrigerator is $700. It takes $100 of electricity to keep it running for a year and the appliance will last 15 years.

    a)Determine the total annual cost of the refridgerator. Include the price of electricity and remember that you have it for 15 Years.

    My question about a, if its asking for annual cost (yearly) why does it tell it to remember we have it for 15 years?

    b) Determine a function that shows the annual cost of the fridge,

    c) Determine the asymptotes in this function? What do they mean in a question like this?
    My answer to c: The asymptotes would have to be x=0 and x=15 because you get the fridge at 0 and it lasts 15 years.

    d) If another brand of refrigerator costs $2000 but lasts 20 years, is it worth it to buy that?
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  2. #2
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    Quote Originally Posted by BabaGurGur View Post
    Hello everyone, I've been trying to solve this question for quite some time but I cannot do it. If anyone can show me how it would be greatly appreciated.

    The cost of a refrigerator is $700. It takes $100 of electricity to keep it running for a year and the appliance will last 15 years.

    a)Determine the total annual cost of the refridgerator. Include the price of electricity and remember that you have it for 15 Years.

    My question about a, if its asking for annual cost (yearly) why does it tell it to remember we have it for 15 years?

    b) Determine a function that shows the annual cost of the fridge,

    c) Determine the asymptotes in this function? What do they mean in a question like this?
    My answer to c: The asymptotes would have to be x=0 and x=15 because you get the fridge at 0 and it lasts 15 years.

    d) If another brand of refrigerator costs $2000 but lasts 20 years, is it worth it to buy that?
    As far as I understand the question you should answer how much you have to pay per year depending on the time the refrigerator is running.
    An example:
    Code:
    operating time     total costs    annual costs
          1                800             800
          2                900             450
          ...              ...             ...
          5                1200           240
    If you use the refrigerator for n years you'll get annual costs of c(n)=\frac{700+100n}{n}
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  3. #3
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    Quote Originally Posted by BabaGurGur View Post
    Hello everyone, I've been trying to solve this question for quite some time but I cannot do it. If anyone can show me how it would be greatly appreciated.

    The cost of a refrigerator is $700. It takes $100 of electricity to keep it running for a year and the appliance will last 15 years.

    a)Determine the total annual cost of the refridgerator. Include the price of electricity and remember that you have it for 15 Years.

    My question about a, if its asking for annual cost (yearly) why does it tell it to remember we have it for 15 years?
    Because you have to include the cost of the refrigerator itself. Imagine saving up to replace the refrigerator in 15 years. If it cost $700 dollars and you have 15 years to save to replace it, how do you have to save each year? (That's what economists call "depreciation"). Add the cost of the electricity to that.

    b) Determine a function that shows the annual cost of the fridge,
    A "function" requires "variables". I assume that they mean you to consider the cost of the refrigerator and cost of electricity to be variables. Again, you need to divide the cost of the refrigerator by 15, then add the cost of electricity.

    c) Determine the asymptotes in this function? What do they mean in a question like this?
    My answer to c: The asymptotes would have to be x=0 and x=15 because you get the fridge at 0 and it lasts 15 years.
    Whoever gave you you this problem expects you to know what "asymptotes" are. From you answer I suspect that you do not. You had better ask your teacher about "asymptotes".

    d) If another brand of refrigerator costs $2000 but lasts 20 years, is it worth it to buy that?
    You have already calculated the "annual cost" of the first refrigerator. Do the same, using 2000 as price rather than 700 and 20 years rather than 15. Which is lower? I presume you can use the same cost of electricity.
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