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Math Help - derivative with words!

  1. #1
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    derivative with words!

    Bacteria in a culture increase at a rate proportional to the number present. An initial population of 200 triples in 10 hours. If this pattern of increase continues unabated, then the approximate number of bacteria after 1 full day is
    I took 200 and multiply by 10 then multiply that with 12, but I got the wrong answer.


    Two objects in motion from t=0 t=3 seconds have positions X lower case 1 (t)= cos (t^2+1) and x lower case 2(t)= e^t/2t. How many times during the 3 seconds do the objects have the same velocity?
    I know you suppose to take the derivative but do something with it.


    The velocity of a particle in motion along a line (for t=>0) is v(t)=ln(2-t^2). Find the acceleration when the object is at rest.
    I took the derivative, so -2t/2-t^2, but I don't know what to do next.
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  2. #2
    Grand Panjandrum
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    Bacteria in a culture increase at a rate proportional to the number present. An initial population of 200 triples in 10 hours. If this pattern of increase continues unabated, then the approximate number of bacteria after 1 full day is?
    take time as measured in hours.

    You are told that the population satisfies the differential equation:

    \frac{dp}{dt}=kp

    for some constant k.

    hence:

     <br />
p(t)=Ae^{kt}<br />

    Put t=0 and we get:

     <br />
p(0)=A=200<br />

    Also we have:

    p(10)=200e^{10k}=600

    so:

    k=\frac{\ln(3)}{10}

    Now evaluate p(24) .

    CB
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