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anonymous

  • 5 years ago

If we have a graph of data which has: Time (t) (hours) verses Ln(Population) and the data goes as follows: Time (hours) - 1 2.5 5 7 12 15 18 Ln(Pop) - (2.89)(3)(3.13)(3.3)(3.61)(3.83)(4.03) Dont mind the brackets^ (just to separate the numbers) The question asks to investigate whether this is an exponential growth pattern =/.. In words how would i explain it is an exponential pattern?

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  1. anonymous
    • 5 years ago
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    Try graphing the points and seeing of the resulting curve is in the form of an exponential.

  2. amistre64
    • 5 years ago
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    plot the points and see what they look like on a graph is my solution

  3. amistre64
    • 5 years ago
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    you can see if its linear by taking the slope between a few points and see if they match

  4. amistre64
    • 5 years ago
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    you could also assume it exponential and try to determine a formula for it

  5. amistre64
    • 5 years ago
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    use discrete recursion equations maybe?

  6. anonymous
    • 5 years ago
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    Lagrange polynomials?

  7. anonymous
    • 5 years ago
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    just shoot me now :P

  8. amistre64
    • 5 years ago
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    y = b*a^x and solve for the solutions?

  9. anonymous
    • 5 years ago
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    I've already graphed it and it looks linear, however,the assignment is based on exponentials =/

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  10. amistre64
    • 5 years ago
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    yes, it does match linearly quite well; but perhaps we are just to close to it so that it looks linear?

  11. myininaya
    • 5 years ago
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    m1=(3.83-3.61)/(15-12)=11/150 m2=(3.61-3.3)/(12-7)=.062 not linear

  12. anonymous
    • 5 years ago
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    Jhonte was able to find a linear formula though?

  13. amistre64
    • 5 years ago
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    jhon found a best fit match; not quite the same as 'its linear'

  14. myininaya
    • 5 years ago
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    are we doing linear regression?

  15. anonymous
    • 5 years ago
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    Yeah thats the best fit.

  16. amistre64
    • 5 years ago
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    the trouble with best fit; is that we learn in calculus that if we look close enough at a curve it becomes straight

  17. amistre64
    • 5 years ago
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    the earthis flat after all :)

  18. anonymous
    • 5 years ago
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    hahah true :P

  19. anonymous
    • 5 years ago
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    So what myininaya post earlier: m1=(3.83-3.61)/(15-12)=11/150 m2=(3.61-3.3)/(12-7)=.062 How does this show it is not linear?

  20. anonymous
    • 5 years ago
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    linear functions have one slope

  21. amistre64
    • 5 years ago
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    linear has the same slopes; those are 2 different slopes

  22. anonymous
    • 5 years ago
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    Oh, okay

  23. anonymous
    • 5 years ago
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    its derivative is a constant, whereas this function's derivate changes signs more than once is not

  24. anonymous
    • 5 years ago
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    it looks like a polynomial to me

  25. anonymous
    • 5 years ago
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    So, if i were to explain this was an exponential growth pattern. I could include why it is not linear and what else could i perhaps add to support this argument?

  26. amistre64
    • 5 years ago
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    donuts; they work good for proving your point :)

  27. anonymous
    • 5 years ago
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    lol

  28. anonymous
    • 5 years ago
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    ahaha

  29. anonymous
    • 5 years ago
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    Thanks to everyone that helped :D <3. Ill just mention why it isn't linear :P!

  30. myininaya
    • 5 years ago
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    ok good luck

  31. anonymous
    • 5 years ago
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    thank you :)

  32. anonymous
    • 5 years ago
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    Oh damn it! is was meant to ask, could you explain to me what Fruitless said earlier: "its derivative is a constant, whereas this function's derivate changes signs more than once is no"

  33. myininaya
    • 5 years ago
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    do you know anything about calculus?

  34. anonymous
    • 5 years ago
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    Yeah, but does he mean to derivative of Ln(population)?

  35. anonymous
    • 5 years ago
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    I meant the slopes increase/decrease variably between points, so I am assuming it is a polynomial.

  36. anonymous
    • 5 years ago
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    Not negatively decrease, I mean decrease relative to the previous slope.

  37. myininaya
    • 5 years ago
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    hey so jhonte, you are going to argue that it is an exponential function right? You could say it is possible since it the function keeps increasing.

  38. anonymous
    • 5 years ago
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    Yeah

  39. anonymous
    • 5 years ago
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    Alright thanks alot :D!

  40. anonymous
    • 5 years ago
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    So, all in all.. An exponential growth pattern increases faster as x increases?

  41. anonymous
    • 5 years ago
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    Not exactly... It is exponential growth as long as the function increases; the slope cannot be less than 0.

  42. anonymous
    • 5 years ago
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    In this case the function increases each time doesn't it?

  43. anonymous
    • 5 years ago
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    Yes. That could be one of your arguments to support that it is an exponential.

  44. anonymous
    • 5 years ago
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    THANKS SO MUCH OMG YOU GUYS ROCK!

  45. anonymous
    • 5 years ago
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    Thanks :)

  46. anonymous
    • 5 years ago
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    One second, sorry for bringing the topic back up, but does the ln of data have to show a linear graph?

  47. anonymous
    • 5 years ago
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    If you are assuming it is exponential, then make a curve "approximation" between each two points.

  48. anonymous
    • 5 years ago
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    I think I've missed an import piece of data in being the Population (millions) 18 20 23 27 37 46 56

  49. anonymous
    • 5 years ago
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    I found the ln(pop) from those

  50. anonymous
    • 5 years ago
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    I'm being told the ln(population) verse time graph must be linear....

  51. anonymous
    • 5 years ago
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    My current argument is: The Ln(Population) verse Time graph at first glance looks linear, however, we are able to prove it is in-fact not linear by finding the gradient at different points and seeing if the gradient is constant. So, to find the gradient we use m= (y2-y1)/(x2-x1) Therefore, we know y = Ln(Population) and x = Time. Now we find the gradient at any random points. m1=((3.83-3.61))/((15-12))=0.73 m2= ((3.61-3.3))/(12-7)=0.62 It becomes evident to as why this is not a linear growth pattern. In-order to be linear the gradient has to be constant throughout. Another key in stating whether a graph is an exponential growth pattern is by indentifying whether the function increases and it’s slope doesn’t equal less than 0. In this case we are able to conclude this is in fact an exponential growth pattern as it’s function does increase throughout.

  52. anonymous
    • 5 years ago
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    I agree with your argument.

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