Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

use discrete recursion equations maybe?

Answer 6

Lagrange polynomials?

Answer 7

just shoot me now :P

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

Jhonte was able to find a linear formula though?

Answer 13

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

Answer 14

are we doing linear regression?

Answer 15

Yeah thats the best fit.

Answer 16

the trouble with best fit; is that we learn in calculus that if we look close enough at a curve it becomes straight

Answer 17

the earthis flat after all :)

Answer 18

hahah true :P

Answer 19

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?

Answer 20

linear functions have one slope

Answer 21

linear has the same slopes; those are 2 different slopes

Answer 22

Oh, okay

Answer 23

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

Answer 24

it looks like a polynomial to me

Answer 25

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?

Answer 26

donuts; they work good for proving your point :)

Answer 27

lol

Answer 28

ahaha

Answer 29

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

Answer 30

ok good luck

Answer 31

thank you :)

Answer 32

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"

Answer 33

do you know anything about calculus?

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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.

Answer 38

Yeah

Answer 39

Alright thanks alot :D!

Answer 40

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

Answer 41

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

Answer 42

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

Answer 43

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

Answer 44

THANKS SO MUCH OMG YOU GUYS ROCK!

Answer 45

Thanks :)

Answer 46

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

Answer 47

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

Answer 48

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

Answer 49

I found the ln(pop) from those

Answer 50

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

Answer 51

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.

Answer 52

I agree with your argument.