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Math Help - Linear Function

  1. #1
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    Linear Function

    In 1995, the life expectancy of males in a certain county was 69.5 years. In 1999, it ws 72.1 years. Let E represent the life expectancy in year t and let t represent the number of years since 1995.

    The Linear function E(t) that fits the data is.
    E(t)=______ t + ______

    Use the Function to predict the life expectancy of males in 2005.

    E(10)=

    Round to the nearest tenth.

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  2. #2
    Super Member Aryth's Avatar
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    Let's say that at t = 0, it is the year 1995, so we know that:

    E(0) = 69.5

    So, at t = 4, we get:

    E(4) = 72.1

    We know that:

    E(x) = at + b

    Where b is the y-intercept, which is E(0), that gives us:

    E(t) = at + 69.5

    Now, all we need to to is set it equal to E(4) to solve for a:

    E(4) = a(4) + 69.5 = 72.1

    4a = 2.6

    a = 0.65

    So, we now have an equation:

    E(t) = 0.65t + 69.5


    And, now we find t = 10:

    E(10) = 0.65(10) + 69.5 = 6.5 + 69.5 = 76

    And there you go.
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  3. #3
    MHF Contributor
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    ok...

    Quote Originally Posted by Aryth View Post
    Let's say that at t = 0, it is the year 1995, so we know that:

    E(0) = 69.5

    So, at t = 4, we get:

    E(4) = 72.1

    We know that:

    E(x) = at + b

    Where b is the y-intercept, which is E(0), that gives us:

    E(t) = at + 69.5

    Now, all we need to to is set it equal to E(4) to solve for a:

    E(4) = a(4) + 69.5 = 72.1

    4a = 2.6

    a = 0.65

    So, we now have an equation:

    E(t) = 0.65t + 69.5


    And, now we find t = 10:

    E(10) = 0.65(10) + 69.5 = 6.5 + 69.5 = 76

    And there you go.
    Great job and easy reading.
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