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Math Help - help cal hw

  1. #1
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    help cal hw

      1. 1) the population of a country doubles every 20 years. if the population (in millions) of the country was 100 in 2002, what will the population be in 2014?

        2) a particle moves along the x axis with a velocity given by v(t)= 2+sint. when t=0 the particle is at x= -2 . where is the particle when t= π (pie)
        a)2π b)π c)π-1 d)π-2 e)π+1

        3) consider the diff.eq dy/dx=(1-2x)y.if y=10 when x=, find an equation for y.

        a) y=e^x-x^2 b)y=10+e^x-x^2 c)y=10e^x-x^2 d)y=x-x^2+10

        please show me how to do these..i want to learn
    Last edited by mr fantastic; December 13th 2011 at 12:27 PM. Reason: Restored deleted question.
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  2. #2
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    Question 1 is fairly straightforward. Since only 12 years have passed the population will only increase by  \frac{12}{20} . So the population will increase by:
     \frac{12}{20} * 100 = 60 \mbox{ people}

    Moving on to question 2. First of all to get your position you need to integrate your formula for velocity and take into account the constant:

     x(t) = \int v(t) dt
     = \int (2 + \sin t) dt
     x(t) = 2t - \cos t + c
    To find the value for the constant use the information given when t= 0, x = -2:
     -2 = 2*0 - \cos 0 + c
     -2 = -1 + c
     c = -1

    Formula for  x(t) = 2t - \cos t -1
    To find where the particle is you just need to put each of the values asked for into the equation in place of t.

    Finally for 3:
    Rearrange the equation so x terms are all on the same side and the same with the y terms
     \frac{dy}{dx} = (1 - 2x)y
     \frac{1}{y} dy = (1 - 2x) dx
    Then integrate to get:
     \ln y = x -x^2 + c
    Rearrange to make find an equation for y:
     y = e^{x - x^2 + c}
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  3. #3
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    for question 1 i got aproximately 151.572

    i did this
    p(t)=100(2^t/20)
    p(12)=100(2^12/20)
    =151.572

    for nmber 2 is it b

    3) it is c right

    just to make sure

    thank u so much for your help
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  4. #4
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    1) the population of a country doubles every 20 years. if the population (in millions) of the country was 100 in 2002, what will the population be in 2014?
    let 2002 be t = 0

    P(t) = 100 \cdot 2^{\frac{t}{20}}

    evaluate P(12)
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