anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Try graphing the points and seeing of the resulting curve is in the form of an exponential.
amistre64
  • amistre64
plot the points and see what they look like on a graph is my solution
amistre64
  • amistre64
you can see if its linear by taking the slope between a few points and see if they match

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amistre64
  • amistre64
you could also assume it exponential and try to determine a formula for it
amistre64
  • amistre64
use discrete recursion equations maybe?
anonymous
  • anonymous
Lagrange polynomials?
anonymous
  • anonymous
just shoot me now :P
amistre64
  • amistre64
y = b*a^x and solve for the solutions?
anonymous
  • anonymous
I've already graphed it and it looks linear, however,the assignment is based on exponentials =/
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amistre64
  • amistre64
yes, it does match linearly quite well; but perhaps we are just to close to it so that it looks linear?
myininaya
  • myininaya
m1=(3.83-3.61)/(15-12)=11/150 m2=(3.61-3.3)/(12-7)=.062 not linear
anonymous
  • anonymous
Jhonte was able to find a linear formula though?
amistre64
  • amistre64
jhon found a best fit match; not quite the same as 'its linear'
myininaya
  • myininaya
are we doing linear regression?
anonymous
  • anonymous
Yeah thats the best fit.
amistre64
  • amistre64
the trouble with best fit; is that we learn in calculus that if we look close enough at a curve it becomes straight
amistre64
  • amistre64
the earthis flat after all :)
anonymous
  • anonymous
hahah true :P
anonymous
  • anonymous
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?
anonymous
  • anonymous
linear functions have one slope
amistre64
  • amistre64
linear has the same slopes; those are 2 different slopes
anonymous
  • anonymous
Oh, okay
anonymous
  • anonymous
its derivative is a constant, whereas this function's derivate changes signs more than once is not
anonymous
  • anonymous
it looks like a polynomial to me
anonymous
  • anonymous
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?
amistre64
  • amistre64
donuts; they work good for proving your point :)
anonymous
  • anonymous
lol
anonymous
  • anonymous
ahaha
anonymous
  • anonymous
Thanks to everyone that helped :D <3. Ill just mention why it isn't linear :P!
myininaya
  • myininaya
ok good luck
anonymous
  • anonymous
thank you :)
anonymous
  • anonymous
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"
myininaya
  • myininaya
do you know anything about calculus?
anonymous
  • anonymous
Yeah, but does he mean to derivative of Ln(population)?
anonymous
  • anonymous
I meant the slopes increase/decrease variably between points, so I am assuming it is a polynomial.
anonymous
  • anonymous
Not negatively decrease, I mean decrease relative to the previous slope.
myininaya
  • myininaya
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.
anonymous
  • anonymous
Yeah
anonymous
  • anonymous
Alright thanks alot :D!
anonymous
  • anonymous
So, all in all.. An exponential growth pattern increases faster as x increases?
anonymous
  • anonymous
Not exactly... It is exponential growth as long as the function increases; the slope cannot be less than 0.
anonymous
  • anonymous
In this case the function increases each time doesn't it?
anonymous
  • anonymous
Yes. That could be one of your arguments to support that it is an exponential.
anonymous
  • anonymous
THANKS SO MUCH OMG YOU GUYS ROCK!
anonymous
  • anonymous
Thanks :)
anonymous
  • anonymous
One second, sorry for bringing the topic back up, but does the ln of data have to show a linear graph?
anonymous
  • anonymous
If you are assuming it is exponential, then make a curve "approximation" between each two points.
anonymous
  • anonymous
I think I've missed an import piece of data in being the Population (millions) 18 20 23 27 37 46 56
anonymous
  • anonymous
I found the ln(pop) from those
anonymous
  • anonymous
I'm being told the ln(population) verse time graph must be linear....
anonymous
  • anonymous
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.
anonymous
  • anonymous
I agree with your argument.

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