1. ## population growth

The problem is a bmp image because I'm no good at writing out the functions on the computer

I graphed the 3 functions, and the 2 difference functions, but I'm not exactly sure what the functions mean - I don't even really understand what these functions predict and I'm not sure at all what my answer should be

thanks a lot if you can help

2. this is a particularly problematic problem because what it looks like to me is that each scientist's predictions are based on a different predicted number of mussels in the area, and the functions are predicting the spread of mussels, which I don't understand.

Can anyone explain what these mean to me?

Also what conclusions would I be able to draw from a difference function? I'm speaking conceptually what could i learn from any given difference function

Thanks so much if you can help, because I really need it

3. Originally Posted by mikedwd

The problem is a bmp image because I'm no good at writing out the functions on the computer

I graphed the 3 functions, and the 2 difference functions, but I'm not exactly sure what the functions mean - I don't even really understand what these functions predict and I'm not sure at all what my answer should be

thanks a lot if you can help
The three functions are three different models of population growth. They could be the results of different methods of fitting an exponential model to measurement data, or to different measurments of the same populations.

What you should observe from the differnces is that the predictions of the models diverge as x becomes large, and that they diverge in different ways and speeds $\displaystyle f_3$ diverging much faster than $\displaystyle f_2$ from $\displaystyle f_1$.

RonL

4. Alright, thanks a lot that seems simple enough (regarding the difference functions)

But I'm still wondering about this: it states that n equals the predicted population of mussels in an area, and x is the number of months passed, so what exactly does f(x) model?

Oh I see all the f(x) models the number of individual mussels (in 1000s) to be living in the lake after x months have elapsed...wow

I was thinking that these graphs were modelling something much more complicated because I got myself caught up in the wording (thought it said n was the population, when f(x) is the population)

Alright thanks a lot for your help, and sorry for my confusion!

5. Wait...does F3 diverge faster from F1 than F2 does?

My difference graph for F3-F1 has the values almost all hugging the x-axis, wouldn't that mean that F3 diverges slowly from F1?

My F2-F1 graph has a large arch and looks similar to the original graphs.

6. Originally Posted by mikedwd
Wait...does F3 diverge faster from F1 than F2 does?

My difference graph for F3-F1 has the values almost all hugging the x-axis, wouldn't that mean that F3 diverges slowly from F1?

My F2-F1 graph has a large arch and looks similar to the original graphs.
Sorry other way around, the difference in exponent is more important than the difference in multipler.

RonL

7. Yeah so my last post is correct, right?

Sorry I need to so much verification I'm just a little on edge. The F2 would diverge faster because the base of an exponent will play a larger role as x approaches infinity than a multiplier would. That sounds right to me...