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Algebra 2

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A company can produce T-shirts for $0.99 each. They spent $1,000,000 on their building and machines. What is the horizontal asymptotes of the graph that models the average cost of each t shirt, including the start up cost?

  • Algebra 2 - ,

    total cost for x shirts is

    c(x) = 1000000 + .99x
    average cost is
    a(x) = c(x)/x = .99 + 1000000/x

    asymptote at a = .99

    makes sense, since for say, a billion shirts, they will each cost .99 + .001

    (the fixed cost is shared among a billion shirts). The average cost will never get below .99, but will get closer and closer to it, as the fixed amount is spread among more and more shirts.

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