Results 1 to 2 of 2

Math Help - A few questions ...

  1. #1
    Junior Member
    Joined
    Sep 2007
    Posts
    55

    A few questions ...

    Hello. I have a few questions I am having trouble with.

    12. A bacterium has 25 cells, and in 10 hours grow to 350. What is the doubling period of the bacteria? Use the formula y=c(a)^t/d


    13. In 1990, at t=0, the population of a city was 48 500. In the year 2000, its population was 50 000. If the population grows exponentially, find the groth rate using the formula P=k(a)^t
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by finalfantasy View Post
    ...14^\frac1{10}}

    12. A bacterium has 25 cells, and in 10 hours grow to 350. What is the doubling period of the bacteria? Use the formula y=c(a)^t/d

    ...
    Hello,

    we have: t_0 = 0,~ y_0 = 25 [1]

    we know: t = 10,~ y_10 = 350 [2]

    Calculate the base first using y = c \cdot a^t

    [1]: 25 = c \cdot a^0~\implies~ \boxed{c=25}

    [2] 350=25 \cdot a^10~\implies~ \boxed{a=14^\frac1{10}}

    If the amount of cells has doubled we have 50 cells. Use all known values to calculate the time:
    50=25 \cdot \left(14^\frac1{10}  \right)^t~\implies~ 2=\left(14^\frac1{10}  \right)^t ~\implies~\ln(2)=\frac1{10} \cdot \ln(14) \cdot t~\implies~ t=10 \cdot \frac{\ln(2)}{\ln(14)}\approx 2.626\ h\approx 2h\ 37\ min \ 35\ s
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. More log questions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 31st 2010, 05:58 PM
  2. Please someone help me with just 2 questions?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 4th 2009, 05:55 AM
  3. Some Questions !
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 3rd 2009, 04:09 AM
  4. Replies: 4
    Last Post: July 19th 2008, 08:18 PM
  5. Replies: 3
    Last Post: August 1st 2005, 02:53 AM

Search Tags


/mathhelpforum @mathhelpforum