## January 11, 2013

### How to analyze growth rate

I know you are agog with curiosity wondering how I am using the quadratic equation.  By using it I feel like I am fulfilling every math teachers dream.  This post will be a bit math heavy - just think of it as a way to ward off dementia.  Plus, this is the whole point of what I am doing, so it's pretty important.
First, the data I'm using is from mizuna planted on September 18th.  Second, remember that I measure growth rate by measuring leaf length of the greens twice a week.  The above chart shows those measures condensed over time.  Each vertical line of dots is one day.  You can see what a range of leaf lengths there are in plants sown on the same day and that as leaf length increases with time.
To clarify that plants grow I added a linear trendline (in red).  Every line is described by an equation.  So, this line is described as:  Leaf length (cm) = -4.02 + 0.64*DAS.  It's nice and neat, and if only I could just stay here.
But, no, it's time to add a quadratic curve (in green). Quadratic equations are curvy, which is why the equations describing them are more complex and involve squared values.  See:
Leaf length (cm) = -3.41 + 0.64*DAS - 0.02*(DAS-21.49)2

The quadratic line fits the data better than the linear line (just trust me), so that's what I should use.
Finally, we've gotten to the point - how to use these equations!  (If you've made it this far I commend you.)  I've determined that the best size for baby salad greens is between 6 and 12 cm (purple dotted lines on the chart above).  Using the linear and quadratic equations I can figure out how many days it takes for mizuna to reach these sizes.  Just looking at the chart, it takes mizuna about 16 days to reach 6cm and about 24 days for it to reach 12cm.  I'd say that is enough for a Friday morning right?