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Math Help - Use a quadractic regression equation to predict population.

  1. #1
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    Use a quadractic regression equation to predict population.

    I was given the population of Las Vegas for every 10 years starting at 1900 and ending in 1990. From these 10 data points I created a table and Graph with my Ti-83.

    I found the quadratic regression equation. P =population t=time since 1900

    P(t)=53.4804t^2-2217.5496t+12820.6454

    I also found the x intercepts and the vertex.
    X=34.5202
    X=6.9445

    The vertex
    X=20.7324
    Y=12820.6454

    Now this is the part where I am stuck. My teacher wants me use to use the above information to determine when will (was) the population of Las Vegas be 1 million people, when was (will) the population be zero? He also said some answers might not be possible with my data(Las Vegas pop)

    So I guess that I need to substitute 1 million into P of my equation and solve for t. Is this right ? If so how would I go about that? or is it something else?

    I appreciate any help and let me know if you need to me to clarify anything...I'm new.
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  2. #2
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    Quote Originally Posted by ghostbuster View Post

    So I guess that I need to substitute 1 million into P of my equation and solve for t. Is this right ? If so how would I go about that? or is it something else?
    Yep, solve as a normal quadratic t = \frac{-b\pm\sqrt{b^2-4ac}}{2a}

    Quote Originally Posted by ghostbuster View Post
    He also said some answers might not be possible with my data(Las Vegas pop)
    This will be for P,t <0
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  3. #3
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    Yep, solve as a normal quadratic
    Could you give me a little more info as how to do that Where would the 1,000,000 go?
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    P(t)=53.4804t^2-2217.5496t+12820.6454

    1000000=53.4804t^2-2217.5496t+12820.6454

    1000000=53.4804t^2-2218t+12821

     0=53t^2-2218t-987179

    Now a = 53, b= 2218 , c= -987179
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  5. #5
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    So I put these into
    and this will give the year that the population will be at 1 million?

    Thanks for the help....I've haven't been in a math class for a couple of years.
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  6. #6
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    Quote Originally Posted by ghostbuster View Post
    So I put these into
    and this will give the year that the population will be at 1 million?
    yep....
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  7. #7
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    when was (will) the population be zero?
    ]
    is this possible?...do I just do the same thing but put in a zero instead of 1 million?
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  8. #8
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    Quote Originally Posted by ghostbuster View Post
    ]
    is this possible?...do I just do the same thing but put in a zero instead of 1 million?
    Could be 0 if gambling became prohibited!

    Otherwise yep put 0 instead of 1 million.

    Note that if b^2-4ac < 0 there will be no solutions.
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