Results 1 to 6 of 6

Math Help - Antidervatives?

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    7

    Antidervatives?

    My lecturer give weekly assignments for our class and each assignment is individual, he also makes a sample sheet with similar questions that we may ask for assistance with tutors and the likes, There's one particular question that has me stumped in my assignment I'm aware that anti derivatives are key to solving the question but I can't figure out how to go about solving it.
    This is the sample sheets version of the question so I'm more interested in the step by step solution than the actual answer. Thanks in advance!




    And just so I can't be accused of trying to get people to do my assignment here's a link to assignment page log in as a guest and choose sheet 6 and you'll see the question there.
    http://alberti.nuigalway.ie:8125/exquery.html
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: Antidervatives?

    Quote Originally Posted by Daithi19 View Post
    My lecturer give weekly assignments for our class and each assignment is individual, he also makes a sample sheet with similar questions that we may ask for assistance with tutors and the likes, There's one particular question that has me stumped in my assignment I'm aware that anti derivatives are key to solving the question but I can't figure out how to go about solving it.
    This is the sample sheets version of the question so I'm more interested in the step by step solution than the actual answer. Thanks in advance!




    And just so I can't be accused of trying to get people to do my assignment here's a link to assignment page log in as a guest and choose sheet 6 and you'll see the question there.
    http://alberti.nuigalway.ie:8125/exquery.html
    Since they have given you the growth rate and a formula for it, just plug and chug.

    r=\frac{1}{N}\frac{dN}{dt} \iff .06dt=\frac{dN}{N}

    Now just integrate both sides of the equation and use the fact that N(0)=3 \times 10^9

    post back if you get stuck!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2011
    Posts
    7

    Re: Antidervatives?

    This problem really has me stuck I'm still not sure how to do it, would you mind doing the problem step by step and explaining each step as you go?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5

    Re: Antidervatives?

    Quote Originally Posted by Daithi19 View Post
    This problem really has me stuck I'm still not sure how to do it, would you mind doing the problem step by step and explaining each step as you go?
    You have been told the differenbtial equation to solve:

    0.6N = \frac{dN}{dt}

    and you have been told that it's seperable:

    0.6 dt = \frac{1}{N} dN.

    And you have been told what to do with it: Integrate both sides.

    Surely you have made some progress. Show what you have done and say where you are stuck.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2011
    Posts
    7

    Re: Antidervatives?

    All right so I integrate
    0.6 dt = \frac{1}{N} dN
    and I end up with
    0.6 t = log (N)
    But I'm not sure where to go from here, do I sub in 35 for t?
    If I do that I end up with N= 1318815734 but that's obviously wrong so I'm still unsure of what to do.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,549
    Thanks
    1418

    Re: Antidervatives?

    Quote Originally Posted by Daithi19 View Post
    All right so I integrate
    0.6 dt = \frac{1}{N} dN
    and I end up with
    0.6 t = log (N)
    But I'm not sure where to go from here, do I sub in 35 for t?
    If I do that I end up with N= 1318815734 but that's obviously wrong so I'm still unsure of what to do.
    First, the antiderivative of \displaystyle \begin{align*} \frac{1}{x}\,dx \end{align*} is not \displaystyle \begin{align*} \ln{x} \end{align*} , it's \displaystyle \begin{align*} \ln{|x|} \end{align*} .

    Second, you have forgotten your integration constant.

    You have been given a point that satisfies the solution to your DE, use it to evaluate the constant.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum