**Carly Rae Jepsen’s “Call Me Maybe” passed Van Morrison’s “Into the Mystic”.**

I’m referring to my iTunes library, of course.

It wasn’t me. Meet the culprits:

First, “Van the Man”. On October 13, 2008, I added “Into the Mystic” to my library (‘Date Modified’ in iTunes). I’m calling this *t* = 0. I’ve played it 62 times. I last played this “song of such elemental beauty and grace” 1284 days later on April 19, 2012.

Jepsen’s up next. “Call Me Maybe” was added (not by me) on February 28, 2012. This is 1233 days after I added “Into the Mystic”. Seventy-five days later, on May 13, 2012, I listened to this sugary pop tune for the 63rd time. This is 1308 days after adding “Into the Mystic”.

NB: Screenshots of the iTunes Summaries for both songs would make a better first act. Here’s the summary for “Call Me Maybe”:

My initial questions were:

- When did this happen?
- Could I have predicted this?
- How will the number of plays compare in the future?

I modelled this situation using a system of linear equations. For the Irish singer-songwriter, we getÂ *p* = 0.05*d*, where *p* is the number of plays and *d* is the number of days. For the *Canadian Idol*, we get *p* = 0.84*d* âˆ’Â 1035.72.

Comparing slopes is an obvious discussion topic. The line for “Call Me Maybe” is much steeper than the line for “Into the Mystic”; the rate of change is 0.84 plays/day versus 0.05 plays/day.

This problem can also be used to explore unit rates. Unit rates can be expressed in more than one way. It’s about what one is one.

I wanted to express the equationÂ *p*Â = 0.84*d*Â âˆ’Â 1035.72 in the formÂ *pÂ *âˆ’ 63 = 0.84(*d*Â âˆ’ 1233). Slope-point form tells a better story than slope-intercept form in this situation but my GeoGebra skills are rusty.

Having students look at their own iTunes libraries might make a better investigation than practicing solving catch-up problems like this:

I assumed that this situation could be modelled using linear relations. For “Into the Mystic”, fair enough. I think this reasonably approximates the real data. Outside of perhaps when I was commenting on Michael Pershan’s blog, I didn’t go through a Van Morrison phase. Van Morrison is in my wheelhouse and “Into the Mystic” is just in the rotation. The number of plays per day is (almost) constant.

For “Call Me Maybe”, this assumption is likely incorrect. The song’s got legs but the instantaneous rate of change has to be decreasing, right?Â For my mental health, I hope it is. That many plays would surely take its toll.

And what if Carly has competition?

What if I modelled this using a logarithmic function? Check this out:

Note that â‰ˆ 5Â½ years after first being added to my library, “Into the Mystic” can be expected to pass “Call Me Maybe”. The natural state of the universe is restored.

**Update:** I learned how to animate my GeoGebra construction. Also, I corrected a math mistake. (What was *my* misconception?)

Whew! I was hoping the log function was coming! Glad to know balance will be returning!

I’m curious about, “I listened to this sugary pop tune for the 63rd time”. Interesting you didn’t say “They listened…”. So, who is the real culprit?

As an idea for a lesson, this is great. I really like the two-points (beginning and present) approach. A follow-up or extension could have them collect some data over time as well.

Marc, I said I *listened* to this not I *played* this. That makes G&K the culprits. I’m just an innocent bystander. *We* listened would have worked too. I’m glad you’re happy with the log function making an appearance. I like how an argument for a linear function can be made for one song but not another. In Math 8-10, I imagine students could be asked to draw a more reasonable graph for Call Me Maybe. Some might come up with the shape of a log function (without having any knowledge of logs, of course).

Nice avatar, btw.