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?

- anonymous

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- anonymous

Try graphing the points and seeing of the resulting curve is in the form of an exponential.

- amistre64

plot the points and see what they look like on a graph is my solution

- amistre64

you can see if its linear by taking the slope between a few points and see if they match

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## More answers

- amistre64

you could also assume it exponential and try to determine a formula for it

- amistre64

use discrete recursion equations maybe?

- anonymous

Lagrange polynomials?

- anonymous

just shoot me now :P

- amistre64

y = b*a^x and solve for the solutions?

- anonymous

I've already graphed it and it looks linear, however,the assignment is based on exponentials =/

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- amistre64

yes, it does match linearly quite well; but perhaps we are just to close to it so that it looks linear?

- myininaya

m1=(3.83-3.61)/(15-12)=11/150
m2=(3.61-3.3)/(12-7)=.062
not linear

- anonymous

Jhonte was able to find a linear formula though?

- amistre64

jhon found a best fit match; not quite the same as 'its linear'

- myininaya

are we doing linear regression?

- anonymous

Yeah thats the best fit.

- 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

the earthis flat after all :)

- anonymous

hahah true :P

- 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

linear functions have one slope

- amistre64

linear has the same slopes; those are 2 different slopes

- anonymous

Oh, okay

- anonymous

its derivative is a constant, whereas this function's derivate changes signs more than once is not

- anonymous

it looks like a polynomial to me

- 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

donuts; they work good for proving your point :)

- anonymous

lol

- anonymous

ahaha

- anonymous

Thanks to everyone that helped :D <3. Ill just mention why it isn't linear :P!

- myininaya

ok good luck

- anonymous

thank you :)

- 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

do you know anything about calculus?

- anonymous

Yeah, but does he mean to derivative of Ln(population)?

- anonymous

I meant the slopes increase/decrease variably between points, so I am assuming it is a polynomial.

- anonymous

Not negatively decrease, I mean decrease relative to the previous slope.

- 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

Yeah

- anonymous

Alright thanks alot :D!

- anonymous

So, all in all.. An exponential growth pattern increases faster as x increases?

- anonymous

Not exactly... It is exponential growth as long as the function increases; the slope cannot be less than 0.

- anonymous

In this case the function increases each time doesn't it?

- anonymous

Yes. That could be one of your arguments to support that it is an exponential.

- anonymous

THANKS SO MUCH OMG YOU GUYS ROCK!

- anonymous

Thanks :)

- anonymous

One second, sorry for bringing the topic back up, but does the ln of data have to show a linear graph?

- anonymous

If you are assuming it is exponential, then make a curve "approximation" between each two points.

- anonymous

I think I've missed an import piece of data in being the
Population (millions) 18 20 23 27 37 46 56

- anonymous

I found the ln(pop) from those

- anonymous

I'm being told the ln(population) verse time graph must be linear....

- 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

I agree with your argument.

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