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Math Help - Function Word Problem

  1. #1
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    Function Word Problem

    A new set of car tires has a tread depth of 8 millimeters. The tread depth decreases 0.12 millimeters per thousand miles driven. Write an equation that gives the tread depth as a function of the distance driven. Then predict at what distance the tread depth will be 2 millimeters.

    Thanks for any help.
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  2. #2
    Senior Member topher0805's Avatar
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    Let's call the tread depth T, and the distance driven d. T as a function of d gives us:

    T(d)

    Note that the maximum tread depth is 8mm. Let's start with that:

    T(d) = 8

    However, it is stated that for every thousand miles driven, that number decreases by 0.12mm. This means that for every mile driven, the tread depth decreases by 0.00012mm. So our function becomes:

    <br />
T(d) = 8 - (0.00012d)

    Now, to find the distance where the tread depth is 2mm we simply have to use our new equation.
    <br />
T(d) = 2

    Therefore:

    <br />
2 = 8 - (0.00012d)

    Now we just solve for d to get:

    d = 50,000
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  3. #3
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    Thanks a lot
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