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Math Help - calculus homework

  1. #1
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    Exclamation calculus homework

    Hey just had a problem regarding rates of change.
    ill post the whole question so there is no confusion.
    " The number of bacteria present in a culture at time t hours after the beginning of an experiment is denoted by N. The relationship between N and t is modelled by N=10(1+3/2t)*3 (that is 10 multiply 1 plus 3 over 2 t to the power of 3) At what rate per hour will the number of bacteria be increasing when t=6?

    im assuming the chain rule must be used but i cant find the other differential i need to use... any help would be greatly appreciated

    thanks
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  2. #2
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    Lexington, MA (USA)
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    Hello, Yesme!

    The number of bacteria present in a culture at time t hours
    after the beginning of an experiment is denoted by N.
    The relationship between N and t is modelled by N=10(1+3/2t)*3
    (that is 10 multiply 1 plus 3 over 2 t to the power of 3)
    At what rate per hour will the number of bacteria be increasing when t=6 ?

    im assuming the chain rule must be used . . . . Yes!
    but i cant find the other differential i need to use. . . . . other differential?
    I assume the function is: . N \;=\;10\left(1 + \frac{3}{2}t\right)^3

    Then: . \frac{dN}{dt} \;=\;30\left(1 + \frac{3}{2}t\right)^2\!\!\cdot\frac{3}{2} \;=\;45\left(1 + \frac{3}{2}t\right)^2

    Now substitute t = 6.

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  3. #3
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    Mar 2008
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    thanks

    oh right, i assumed that you had to find another differential where it was something like:

    dN/dx multiply dx/dt so then u get dN/dt but i guess i never read the question properly....oops
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