Booming Business Dr. Eyelovedogs and Melovecats' Business at an All Time High

Hi there! Looks like our previous data sorta revealed the future of Dr. Eyelovedogs and Melovecats' business - sorta. We were right about it increasing throughout the year, but not this much...

Word got out about how good the clinic is over here that it's affected the rates of Dr. Doggssuck's clinic, almost wiping him out completely. Here's what my data reveals:

We're measuring Dr. Doggssuck's clinical visits by the average rate of people per month. And by the looks of the graph, in about 16 months from when he started to lose business, he might be a goner.

A quick important note about this data is that it's a little more complicated, but I went ahead and restricted the original derivative down to these points to better show the present results. Here is the original derivative:

Let's go ahead and dissect this a bit while Dr. Eyelovedogs and Melovecats neuter their patients.

Table

Just to give us a base for our findings, here's a table displaying the rate of patients per month separated into five subintervals (think of it as n - 1, if you count the cells) with the left endpoint being 1 and the right endpoint being 16. This table also shows us that we are working every three months, up until the rate is so small it's almost as if there are no returning patients per month.

What we can do is actually estimate how many patients Dr. Doggssuck may have had using what's called a lower & upper estimate.

To gain an upper estimate, we gather all of our higher values and multiply them by the change in time (3 months). We get about 101 patients, because we can't have a 60th of a dog (we can but that's seems a little cruel to the guy). The same for our lower estimate, we gather our lowest values and multiply by our change in time. We get about 50 patients here. Then we average them out like so, and see Dr. Doggssucks average about 75 patients, not bad!

From here let's go ahead and make two graphs of how this can look for Dr. Doggssuck's business...

Left-Hand Sum

When we graph our left-hand sum we go ahead and grab the values to the left of our table, regardless if their value is high or low. In this unfortunate case, we're graphing the points of Dr. Doggssucks' slowly decreasing business rates. But another to view this is by viewing our upper estimate, as it was alongside the left of our table whilst also holding our greater values too. What this upper estimate (left-hand sum) tells us the maximum amount of patients that can be estimated - about 101 patients.

Right-Hand Sum

When graphing a right-hand sum, we graph the values to the right of our table. That said, this happens to be our lower estimate values, which can be seen as the lowest amount of patients Dr. Doggssucks may have had - which is about 50 patients. When we average these two values, we get the points directly on the line, which also can equate to our average value of 75 patients.

All-in-all, this was pretty straightforward...Dr. Doggssuck's business is declining. We see this with how his patients per month rate began to plummet to near 0 patients per month, which is no good for him - but good for Dr. Eyelovedogs and Melovecats! Maybe there was more of a reason why Dr. Doggssucks' business was declining, but that's something for another day. Let's go show the dog-tors our findings!