I must have missed this lecture

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In summary, the conversation is about a mathematical model of bacterial growth over a short period of time. The model, n=10^10(xsin2x+tan^4x^7)^3, is being tested with numerical data and is shown to be a good fit. The question is then posed to determine the rate of bacterial growth after 3 minutes, which can be found by calculating the derivative of the function with respect to time.
  • #1
monet A
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I have a question here that I do not understand completely.
The Growth of virulent bacteria is modeled 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:
 
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  • #2
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?
 
  • #3
That would be parametric differentiation yes?
Thankyou Dan for your help again.
:biggrin:
 
  • #4
monet A said:
That would be parametric differentiation yes?
Thankyou Dan for your help again.
:biggrin:

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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