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Math Help - Exponential growth of bacteria

  1. #1
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    Exponential growth of bacteria

    The number of of bacteria N in a colony after t minutes is given by N=10 000e^{0.05t} Find the rate at which the colony increases when

    i) t=10

    ii) N=2000
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  2. #2
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    Quote Originally Posted by nerdzor View Post
    The number of of bacteria N in a colony after t minutes is given by N=10 000e^{0.05t} Find the rate at which the colony increases when

    i) t=10

    ii) N=2000
    natural exponential growth ...

     <br />
\frac{dN}{dt} = 0.05N<br />
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  3. #3
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    Quote Originally Posted by skeeter View Post
    natural exponential growth ...

     <br />
\frac{dN}{dt} = 0.05N<br />

    Care to explain further?
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  4. #4
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    The number of of bacteria in a colony after minutes is given by Find the rate at which the colony increases when

    i)

    Differentiate 0.05*1000 N'=500e^0.05(10)=824.36

    ii)

    2000=500e^0.05
    4=e^0.05
    In4=Ine^o.o5

    In4/0.05=27.7
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  5. #5
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    In a certain bacteria culture, the rate of increase is proportional to the number of bacteria present

    a) If the number doubles in 3 hours. Find the hourly growth rate
    b) How many bacteria after 9 hours? If the original population is 104
    c) After how many hours are there 4 * 10^4 bacteria
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  6. #6
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    Quote Originally Posted by BobCalc View Post

    ii)

    2000=500e^0.05
    4=e^0.05
    In4=Ine^o.o5

    In4/0.05=27.7
    How odd. The answers say 1000/min
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