## My favorite animals live ‘this’ long

21/01/2012 § 5 Comments

Sometimes we should all stop and wonder how wonderful of a life we have. Other times, we should stop and wonder how wonderful of a life all the animals around us have. Humans are lucky. We all have the ability to live ‘til around 70-years-old while most animals usually live up to 15 – 20 years old tops. The lifespan of an animal – mammals, in this case – can be determined by their heart beats. Typically, the slower the heart rate, the longer the mammal will live. This relationship is, in completely mathematical terms, an **inverse variation relationship**. Less of something means more of something else.

The graphing process was not frustrating at all, contrary to what I’d expected. I set up sliders as seen in the below image at the top of the image. The lines with *a*, *h* and *k* above each line helped me move around my graph in order to fit the points I inserted with the data I gathered from the heart-rate website with all the information.

Of course, it was not easy to find a perfect position for the graph where the line passed each dot but I did my best to find the right trend. Also, we need to take into account that I am actually missing half of the information. The person sitting next to me, Grace, shared the set of data with me and we took half of the information each. Thus, I am missing some data that could help shape the graph better. Despite this though, I think the trend I have presented in my graph is still legitimate and very close to accurate.

The final equation of this graph was *y = 1596.6 ÷ x*.

It’s domain: *x* > 0 and it’s range: *y* > 0. We can find the domain and range because these values are directly linked to the asymptotes. In this graph, the vertical asymptote is 0 on the *x*-axis, and the horizontal asymptote is 0 on the *y*-axis. Because it is not possible to have a negative lifespan and negative heart rate, it is clear that both values must be positive therefore the graph can only be in Quarter I (positive* x*, positive *y*). The asymptotes are the barriers for the graphs and now we know that even if the graph will extend upwards forward and to the right forever, the line will never touch 0. Because of this, any value of *y = 1596.6/x* will always be greater **but never** 0.

This makes sense in mathematical and realistic logic. Realistically, the fact that any value of this equation can’t equal zero makes sense because you can’t have a heart rate of *0* and still live (when *x* = 0). At the same time, you can’t have a lifespan of *0* and still have a heart rate (when *y* = 0). When there is one, there also must be the other.

In fact, although the graph will never touch either *x-* or *y-*axis, the graph will extend as far as it can without touching the asymptote, in this case the axes, the numbers will still grow, even if it’s only by a little. As the graph gets closer to the vertical asymptote, for example, this means that the life span grows by more while the heart rate decreases by only a little. This could make sense in real life. Notice point *F* on the graph is just to the right of point *H* but *H* is much higher compared to point *F*. Think of it like the rise-and-run (aka think of the slope of the line that connects points *H* and *F*). The slope is steeper, meaning the rise is greater than the run. If the rise is greater, it means the change in life span is more than the change in heart rate. It is just vice versa with the other values; the more the change in heart rate, the lower the life span. This also makes sense because the faster a mammal’s heart rate is (see the slope of points *A* and *E*), the shorter amount of time they’ll live. This makes sense if especially if you think about exercise. The faster one’s heart rate is (according to Mr. Rabb), the more chance he or she might have heart disease. This applies greatly to this inverse variation relationship.

Other examples of inverse variation relationships are really basic ones – the greater the diameter of a cylinder, the lower the height of the same amount of water in another cylinder. Pressure and temperature are also inversely related to each other. In economics, the lower the agriculture percentage in a country, the greater it’s GDP is. There are surely other inverse variation relationships; examples you will see in other peoples’ blogs and assignments.

That was a joke.

I like the joke!

Kari I always enjoy reading your posts and other assignments: you put your personality into them and it makes great reading for me! So thank you for that, it is much appreciated.

I also like how you rephrase the inverse variation “less of something means more of something else”. You would make a good teacher!

Good use of diagrams, tables, and of course images, to enhance the quality of the assignment.

One contradiction I do not understand: you have given the equation, and together with your verbal explanations, you seem to be stating that the asymptotes are at 0. However, on the graph, different values of a, h and k are given.

You have considered whether your results make sense, and also done an in-depth analysis of the difference between points F and H.

Nice work, Kari, this was a pleasure to read.

I will post more thorough and detailed feedback, along with your score, on Moodle and Powerschool in a few days’ time.

Hi Ms. Durkin, thanks for pointing out the flaw in the graph. I had actually taken an updated screenshot from when I changed the graph and values but I guess I forgot to use the newer image. I’ve changed it now as well as added links for the images I’ve used. So glad you like this post!

Ok I will go through it again.

One thing, though. Do remember that you need to cite the photo credits. That is an important detail you cannot omit. It is a way of acknowledging gratitude to that person for having the photo available for you to use.

Ok that is better. And there are coloured points this time! 🙂