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I must have missed this lecture

  1. May 1, 2005 #1
    I have a question here that I do not understand completely.
    The Growth of virulent bacteria is modelled over a short period of time by a very ambitious mathematical modeller as n=
    [tex] 10^{10} (x sin2x + tan^4 x^7)^3 [/tex]
    where x is measured in hours from x=.02 --> x= .1 from 12 noon.

    The researcher observes that 1 minute and 12 seconds after noon n = 5 by three minutes after 12 noon n = ca 1250 and by 6 mins after noon the n = ca 78415. Show the model as proposed is a good fit for the numerical data. Determine the rate of Bacterial growth after 3 minutes.

    I am not sure what I am being asked to do here. Am I just plugging in x values for the first half of the question or am I being asked to make a more complex analysis of the function between the said points. And for the second part of the question I presume that n (6) = 78415 is not a good fit for the function, but where shall I start to find a function that does fit, I am not sure of the method I should be employing here, I must have missed the lecture. Please help :confused:
     
    Last edited: May 1, 2005
  2. jcsd
  3. May 1, 2005 #2

    OlderDan

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    The first part is just calculating the values for n at three values for x. They all fit reasonabley well. You do not need to look for a new function. What you need to do is use the given function to determine the RATE of change of n at 3 minutes. How do you find the rate of change of a function of time?
     
  4. May 1, 2005 #3
    That would be parametric differentiation yes?
    Thankyou Dan for your help again.
    :biggrin:
     
  5. May 2, 2005 #4

    OlderDan

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    I'm not sure where you are seeing anything parametric. x is time and you have a function of x, n(x). The rate of change of the function with respect to time is the derivative with respect to x, dn/dx.
     
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