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Math Help - Germfarm math

  1. #1
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    Germfarm math

    in a germfarm the germs increase exponentically that means after every 20 minutes the germs double in quantity.

    a) at 12 oclock the germs are 700. how many are they at 15 oclock?

    B) how many where they at 10 oclock?

    c)Whats the clock when the germs are 1 000 000?


    Thanks again guys need a quick answer, Please the whole calculation not only the answers guys. Im in deep ****.
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  2. #2
    GAMMA Mathematics
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    Quote Originally Posted by Rambo View Post
    in a germfarm the germs increase exponentically that means after every 20 minutes the germs double in quantity.

    a) at 12 oclock the germs are 700. how many are they at 15 oclock?

    B) how many where they at 10 oclock?

    c)Whats the clock when the germs are 1 000 000?


    Thanks again guys need a quick answer, Please the whole calculation not only the answers guys. Im in deep ****.
    f(t)=2^{3t} A

    Let t = 0 denote noon/1200/12:00PM

    f(t)=2^{3t} 700

    Plug t = 3 for 1500/3:00PM and t = -2 for 1000/10:00AM
    Last edited by colby2152; March 11th 2008 at 07:24 AM.
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  3. #3
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    hmmm

    Quote Originally Posted by colby2152 View Post
    f(t)=2^{t/20} A

    Let t = 0 denote noon/1200/12:00PM

    f(t)=2^{t/20} 700

    Plug t = 3 for 1500/3:00PM and t = -2 for 1000/10:00AM
    Shouldnt the solution be f(t)=2^{9} 700 =358400
    because thr population doubles every 20 minutes that means in 3 hours 12-15 it doubles 9 times?
    And b)  f(t)=2^{-6} 700= 10,9375
    Becaus 10-12 is 2 and bacwards -2 hours and the germs double 6 times in 2hours?
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  4. #4
    GAMMA Mathematics
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    Quote Originally Posted by Rambo View Post
    Shouldnt the solution be f(t)=2^{9} 700 =358400
    because thr population doubles every 20 minutes that means in 3 hours 12-15 it doubles 9 times?
    And b)  f(t)=2^{-6} 700= 10,9375
    Becaus 10-12 is 2 and bacwards -2 hours and the germs double 6 times in 2hours?
    I fixed it up... not sure what I was thinking with the time parameter, but you are right, it should be 3t! Good job pointing that out!
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  5. #5
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    Quote Originally Posted by colby2152 View Post
    I fixed it up... not sure what I was thinking with the time parameter, but you are right, it should be 3t! Good job pointing that out!
    Thats what i tought too any idea how i should get to know when the germs are 1000 000?
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  6. #6
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    At 15:20 = 716800 germs
    At 15:40 = 1433600 germs, so in 20minutes 716800 germs born, divide that by time.

    716800/1200=597.333 germs/persec. 1000000-7168000=283200 germs neeeded. So 283200/597.333=474 secs to produce them.

    474/60=6mins54secs. So 15:20+6m54secs=

    15:26:54 as my answer. Others may see it different, I'm just getting back into things so I hope it helps.
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  7. #7
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    Quote Originally Posted by Rambo View Post
    Thats what i tought too any idea how i should get to know when the germs are 1000 000?
    With your question the number of germs is calculated by:

    g(t) = 700 \cdot 2^{3t} t in hours.

    1,000,000 = 700 \cdot 2^{3t}~\iff~\frac{10000}{7} = 2^{3t} . Logarithmize using the ln-function:

    \ln\left(\frac{10000}{7}\right) = 3t \cdot \ln(2)~\iff~ 3t = \frac{\ln\left(\frac{10000}{7}\right)}{\ln(2)} and therefore:

    t = \frac{\ln\left(\frac{10000}{7}\right)}{3 \cdot \ln(2)}\approx 3.49345... and

    3.49345.. h \approx 3h\ 29 min\ 36.4 s
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  8. #8
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    ^^^^^ Much prettier than mine, and I'm sure more accurate. Nice work earboth.
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  9. #9
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    Quote Originally Posted by Tally View Post
    At 15:20 = 716800 germs
    At 15:40 = 1433600 germs, so in 20minutes 716800 germs born, divide that by time.

    716800/1200=597.333 germs/persec. 1000000-7168000=283200 germs neeeded. So 283200/597.333=474 secs to produce them.

    474/60=6mins54secs. So 15:20+6m54secs=

    15:26:54 as my answer. Others may see it different, I'm just getting back into things so I hope it helps.
    The number of germs does not increase by the same amount every 20 minutes
    but doubles every 20 minutes. This is is results in a very much faster growth in
    the population and this is the point of questions like this.

    This is exponential growth.

    RonL
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  10. #10
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    Ah yes... After 20 years I decide to head back to school to become a high school math teacher. Hope I didn't leave it too late.

    Any good sites where I can read up on stuff like this?
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  11. #11
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    Quote Originally Posted by Tally View Post
    Ah yes... After 20 years I decide to head back to school to become a high school math teacher. Hope I didn't leave it too late.

    Any good sites where I can read up on stuff like this?
    Wikipeadia is very good for maths topics as is mathworld

    RonL
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