Results 1 to 3 of 3

Math Help - Help with physics word problems

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    43

    Help with physics word problems

    Hi!

    I am having a lot of trouble with these word problems in the modeling part of my differential equations books. Here is one I am just lost on. I think the wording is throwing me off. Shouldn't I approach this as a homogenous first order ODE, with an initial value???

    Bacteria is being cultured for the production of medication. Without harvesting the bacteria, the rate of change of the population is proportional to its current population, with a proportionality constant of .2 per hour. Also, the bateria are being harvested at a rate of 1000 per hour. If there are initially 8000 bacteria in the culture, solve the initial value problem:

     <br />
(dN/dt) = .2N - 1000<br />

    for the number N of bacteria as a function of time and find the time it takes for the population to double its initial number.

    Thanks for any guidance suggested.
    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
    Quote Originally Posted by kpizle View Post
    Hi!

    I am having a lot of trouble with these word problems in the modeling part of my differential equations books. Here is one I am just lost on. I think the wording is throwing me off. Shouldn't I approach this as a homogenous first order ODE, with an initial value???

    Bacteria is being cultured for the production of medication. Without harvesting the bacteria, the rate of change of the population is proportional to its current population, with a proportionality constant of .2 per hour. Also, the bateria are being harvested at a rate of 1000 per hour. If there are initially 8000 bacteria in the culture, solve the initial value problem:

     <br />
(dN/dt) = .2N - 1000<br />

    for the number N of bacteria as a function of time and find the time it takes for the population to double its initial number.

    Thanks for any guidance suggested.
    This is a first order seperable ODE so

    \frac{dN}{.2N-1000}=dt \iff \frac{dN}{N-5000}=.2tdt Now just integrate to get the equation for N(t)

    Use the inital condition N(0)=8000 to find the arbitary constant then you want to use the equation to find t such that

    N(t)=16000
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    43
    Quote Originally Posted by TheEmptySet View Post
    This is a first order seperable ODE so

    \frac{dN}{.2N-1000}=dt \iff \frac{dN}{N-5000}=.2tdt Now just integrate to get the equation for N(t)

    Use the inital condition N(0)=8000 to find the arbitary constant then you want to use the equation to find t such that

    N(t)=16000

    Thank you so much for your reply.

    After thinking about awhile, I realized I was wrong in my thoughts.

    I finally came up with N(t) = 5000 + 3000 e^(.2*t) as my equation and that t = 6.496 hours to get the population to double.

    Thanks again for your reply!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. please help with these physics problems
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: April 11th 2009, 09:41 AM
  2. Replies: 1
    Last Post: January 8th 2008, 09:46 PM
  3. 2 physics problems
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: September 1st 2007, 08:08 PM
  4. 6 more... physics problems
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: August 29th 2007, 10:40 PM
  5. A few more physics problems I need help with...
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: June 28th 2007, 09:59 PM

Search Tags


/mathhelpforum @mathhelpforum