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: Population growth using logarithims

  1. Jan 25, 2010 #1
    1. The problem statement, all variables and given/known data

    A culture begins with 100,000 bacteria and grows to 125,000 bacteria after 20 min. What is the doubling period to the nearest minute?

    2. Relevant equations


    3. The attempt at a solution

    I can get make the first part out. 125000=100000(rate)^2 I have a feeling its wrong but its as far as i can get.
  2. jcsd
  3. Jan 25, 2010 #2

    Char. Limit

    User Avatar
    Gold Member

    Well, yeah. The doubling period is time, and it's supposed to be the thing you're solving for.
  4. Jan 25, 2010 #3
    So would my rate be 2? if so then would this be right 120000=100000(2)^t

    What confuses me is when it says doubling period, is that time or the rate?
  5. Jan 25, 2010 #4

    Char. Limit

    User Avatar
    Gold Member

    Well, start with this:

    The original is 100,000 and it changes to 125,000 in 20 minutes. So, first solve for the rate, then put in the rate to the equation 200,000=100,000(rate)^(time)
  6. Jan 25, 2010 #5
    Well i can get this far but i cant get farther sorry.
    log (125000/100000)=20log r

    I don't know how to go farther, if r had a value and i was solving for time i would have no problem with this.
  7. Jan 25, 2010 #6
    alrighhhht worked it out on my own :)

    I figured, why log to find the rate, 20th root it.

    (20th root) 1.25=r

    log 2/log1.01=t
    t=62 minutes which is the answer in the back of my textbook. Thanks for setting me on the right path Char.Limit :D
  8. Jan 25, 2010 #7

    Char. Limit

    User Avatar
    Gold Member

    No problem. And it's true... roots are almost always easier than logs.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook