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Math Help - problem solving on function!

  1. #1
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    Thumbs up problem solving on function!

    Pollution control has become a very important concern in all countries. If controls are not put in place, it has been predicted that the function P=10000t^5/4 + 14000 will describe the average pollution, in particles of pollution per cubic centimeter, in most cities at time t, in years,where t=0 corresponds to 1970 and t=37 correspond to 2007. Predict the pollution for 2007, 2010 and 2020.

    Any idea would be helpful at this point!!! Thanks!
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  2. #2
    Member eXist's Avatar
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    Well first we need to find out what those years represent in terms of t:

    So:
    2007 - 1970 = 37 = t_1
    2010 - 1970 = 40 = t_2
    2020 - 1970 = 50 = t_3

    Then we substitute these back into the equation given for the pollution:

    P=10000(37)^{5/4} + 14000 = ?
    P=10000(40)^{5/4} + 14000 = ?
    P=10000(50)^{5/4} + 14000 = ?

    See how those numbers come out.
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  3. #3
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    Quote Originally Posted by lolalovepink View Post
    Pollution control has become a very important concern in all countries. If controls are not put in place, it has been predicted that the function P=10000t^5/4 + 14000 will describe the average pollution, in particles of pollution per cubic centimeter, in most cities at time t, in years,where t=0 corresponds to 1970 and t=37 correspond to 2007. Predict the pollution for 2007, 2010 and 2020.

    Any idea would be helpful at this point!!! Thanks!
    This is a problem of simply plugging in values (substitution).

    If the function is P=10000\cdot t^{5/4} + 14000 and if 2007 is represented by t=37 (because the function models the population of 1970 when t=0), then we simply must replace the t in the function with 37:

    P=10000\cdot37^{5/4} + 14000

    Just do the math out, and we get P=926541 (I think, I'm not sure if you mean t^{5/4} or \frac {10000t^5}{4})

    If t =0 in 1970, then if we want to calculate to population for 2010, we simply find the difference between 2010 and 1970, which is 40 years. So t= 40

    Plug in the number: P=10000\cdot40^{5/4} + 14000 and solve. I think you can figure out the last one.
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