MHB Calculating Logistic Growth Rate

[andre6051]

I have a logistic growth problem. I know this because there is an upper limit of approximately 21,000 people. I need to calculate growth rate. Would it be something as simple as taking two populations and dividing them to get the rate (X2-X1/X1) to obtain it or is there an equation I am missing? I feel like the growth rate is harder to find than that. Plus, for some reason, the number shot up in 2015 and I don't know what to do. The only info I have is below. Thanks!

Example

X Y
44 2010
61 2011
79 2012
208 2013
326 2014
6663 2015

 

[I like Serena]

I have a logistic growth problem. I know this because there is an upper limit of approximately 21,000 people. I need to calculate growth rate. Would it be something as simple as taking two populations and dividing them to get the rate (X2-X1/X1) to obtain it or is there an equation I am missing? I feel like the growth rate is harder to find than that. Plus, for some reason, the number shot up in 2015 and I don't know what to do. The only info I have is below. Thanks!

Example

X Y
44 2010
61 2011
79 2012
208 2013
326 2014
6663 2015

Hi andre6051! Welcome to MHB! (Smile)

It looks like Y is a year and X increases exponentially.
So the relevant equation would be $X=AB^Y$ so that $\frac {X_2}{X_1} = \frac{AB^{Y_2}}{AB^{Y_1}} = B^{Y_2 - Y_1}$.
For successive years that means $B = \frac {X_2}{X_1}$.

It also means that $\log X = \log A + Y \log B$.
Typically we would find a linear regression between $\log X$ and $Y$ to figure out the relation.

Then again, as you already noticed, in 2015 the number shot up, causing an outlier.
We should get more information why that is, since it may mean we can't treat it as a logistic growth problem.
Can it be that the last X should really be, say, 663? Maybe there is a typo...