Results 1 to 4 of 4

Math Help - Pre-calc amoeba doubling every 4 days

  1. #1
    Newbie
    Joined
    Jan 2012
    Posts
    9

    Pre-calc amoeba doubling every 4 days

    A single-celled amoeba doubles every 4 days. How long would it take one amoeba to produce a population of about 10,000 amoebae?


    I have this problem up above....

    I have come up with my own formula, so I posted it on my facebook, then all of a sudden I got 20 or so replies on different formulas. Can you guys help me decide which could be right? I really feel like my formula is right.

    1. My formula 4 ( ln 10000 / ln 2) = 13.2877*4= 53.15 days....
    I used this as proof on wolfram alpha. 2^x = 10000, and it came to 13.2877 or so, then I multiplied by 4.

    2. A friend says this
    4 ( ln 10000 / ln 2) + 4 = 57.15084 days which he used this as proof....
    (2^(57.15084 / 4)) / 2 = 9 999.98351
    thats about 10000

    3. Another friend says this

    10,000 = 4(2)^(t/4)
    2500 = 2^(t/4)
    log 2,500 = (t/4) log 2
    4 log 2,500 / log 2 = t
    t = 45.15 days <==ANSWER

    4. Then finally this guy shows up out of nowhere and does this....
    P = Po*e^(k*t)
    P=pop after time
    Po= original population
    k= rate constant
    t=time
    2Po = Po*e^(k*4)
    2 = e^(k*4)
    ln(2) = k*4
    k = (1/4)ln(2)
    k = 0.173

    10000 = (1)e^(0.173*t)
    ln(10000) = 0.173*t
    t = 53.2 days
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Pre-calc amoeba doubling every 4 days

    This is how I would solve it (essentially as you did):

    P(t)=2^{\frac{t}{4}}=10000\,\therefore\,\frac{t}{4  }=\log_2(10^4)=4\log_2(10)\,\therefore\,t=16\log_2  (10)

    Using the change of base formula, we may write:

    t=\frac{16\ln(10)}{\ln(2)}\approx53.15
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2012
    Posts
    9

    Re: Pre-calc amoeba doubling every 4 days

    Awesome, thanks for the quick reply.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    643

    Re: Pre-calc amoeba doubling every 4 days

    Hello, Nickod777!

    A single-celled amoeba doubles every 4 days. How long would it take
    one amoeba to produce a population of about 10,000 amoebae?

    My formula: . 4\frac{\ln 10,\!000}{\ln 2} \:\approx\:53.15 days. . You are correct!

    The population function is: . P(t) \:=\:2^{\frac{1}{4}t} .where t is measured in days.

    We have: . 2^{\frac{1}{4}t} \:=\:10,\!000

    Take logs (base 10): . \log(2^{\frac{1}{4}t}) \:=\:\log(10,\!000)

    . . . . . . . . . . . . . . . . \tfrac{1}{4}t\log(2) \:=\:4

    n . . . . . . . . . . . . . . . . . . . . . t \:=\:\frac{16}{\log(2)} \:=\:53.15084952
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Doubling a roulette bet
    Posted in the Statistics Forum
    Replies: 0
    Last Post: May 25th 2012, 02:02 PM
  2. Replies: 8
    Last Post: February 11th 2011, 08:59 AM
  3. Doubling time!
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 23rd 2008, 08:50 PM
  4. doubling
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: May 18th 2007, 03:40 PM
  5. Amoeba-doubling problem, help please
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 10th 2006, 08:53 AM

Search Tags


/mathhelpforum @mathhelpforum