1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: ODE bacterial growth problem

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data

    A cell of some bacteria divides into two cells every 40 minutes. The initial population is 2 bacteria.

    a)Find the size of the population after t hours
    b) Find the size of the population after 6 hours.
    c) When will the population reach 12?

    2. Relevant equations

    None given.

    3. The attempt at a solution

    taking t = time in hours, y(t) = population,

    we say that

    dy/dt = (3/2)y --- the 3/2 converts from hours to the 40 min growth period
    dy/y = (3/2)dt
    ln(y) = (3/2)t + C --- C is arbitrary constant
    y = [e^( (3/2)t )] * L -- L is arbitrary constant analogous to e^C.

    we know that y(0) = 2, so to solve initial value problem,

    2 = 1*L

    therefore L = 2

    and the solution for part a) should be y(t) = 2 e^[(3/2)t]

    but this solution is unfortunately incorrect and I don't see how to fix it. Of course it holds for y(0) as it should, but it falls apart when I check other values. a friend mentioned something about "adding or subtracting a 1" somewhere but I don't see where I would do that, and even if I did I wouldn't understand the justification.

    Any help is appreciated, thanks!
  2. jcsd
  3. Feb 8, 2010 #2
    Look at your ODE. It's missing something. The population _DOUBLES_ every 40 minutes. You seem to have forgotten about this fact.

    A suggestion: convert to hours at the very end.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook