I'm working on a math project about a track and field olympic event. The question is, is the relationship between the years and time values linear or exponential?

Question

I'm working on a math project about a track and field olympic event.  The question is, is the relationship between the years and time values linear or exponential?

So I selected an event and I can see that as the years have passed, the time has decreased, so I consider that linear.

Then I have to find a line of best fit for my data and state what the meaning of the slope from that equation is.  I believe the slope represents the change in time in the event each time there is an olympics held.  (Is that correct?)

Here is the question that I am really struggling on:  does my graph have a y-interecept.   Well I know it's not going to have a x-interecept, where the line crosses the x axix because that would mean that they are doing the event in no time which, of course, is impossible.

But what about a y-intercept?

My confusion, I believe, is because the equation of a line is y = mx + b, with b being the y interecept.  I have a "b" in my equation, but would there really be a y intercept in this type of scenario?

Thank you.

scott · Answer

sure ... b represents the first (modern) olympics

the time in the event is dependent on the year of the games

one would expect the times to decrease as a result of improvement of the atheletes
... better conditioning, better nutrition, ... etc.

carly · Answer

I am a little confused by your comments --

My equation of best fit, determined by the computer, is: Y=-.02496x+551.65

My event is 100M mens backstroke, and the first time they did this, in 1906, the time was 1:16.8 which would be 76 secons -- so I don't understand how the b can be the first olympics time.

I understand and agree that the times decrease as time goes on, but I'm still trying to understand this y-intercept thing.

Thank you for clarifying for me.

scott · Answer

how have you defined your variables?

winning time in seconds? ... this should be y

year of games? ... or years since 1st "modern" games? ... this should be x

going back in time beyond the "modern" games is probably meaningless

carly · Answer

Yes, the years are my x and the time in seconds is my y - The question is, is there a y-intercept - so technically, there WOULD be a y-intercept since the line would cross the y-axis??