Predicting The 2050 Olmypics Results

Algebra Level 2

This is a chart of the world record time in the men's 100 meters freestyle, from 1905 to 2010. The x-axis indicates the year when the previous record was broken, and the y-axis indicates the new time taken (in seconds). Times have been decreasing over the years, due to better training techniques and developments in the sport.

Based on the above data, which of the following would be the best prediction of the world record time for the men's 100 meters freestyle in 2050?

Data: Wikipedia

47 55 43 35

9 solutions

Joynob Siddiqua
Jan 13, 2014

2010 corresponds to a value approximately 47 and therefore it can be predicted that in 2050 the record should be less than 45 and greater than 40 according to the plot and hence 43 :)

each time difference of 5 seconds takes place in approximately 15 to 20 years...so according to this assumption..the only possible answer is 43 :D

Parth Viradia - 7 years, 4 months ago

Each time difference of 5 seconds takes place in approximately 15 to 20 years...So according to this assumption..the only possible answer is 43...

Sampad Kar - 7 years, 4 months ago

But why the time would not go below 40 seconds.

Zakaria Ameen - 7 years, 4 months ago

If u try to fit a linear line following the pattern given, it will show that 2050 corresponds to a value somewhat 43

Joynob Siddiqua - 7 years, 4 months ago

Also this is not linear, more like exponential, since then in like year 3000 people would have negative times.

William Cui - 7 years, 4 months ago

@William Cui – The years 1920 and 1980 give clean data as 60 and 50. forming a linear equation of those gave me an answer of around 39. I chose 35 hence and the answer was deemed wrong.

Soaham Ganguly - 7 years, 4 months ago

@Soaham Ganguly – no need of a lenear equation dude...cuz the data is not perfect..u need to try and analyze it through your vision..a perfect answer is impossible..only assumption is possible. :D :)

Parth Viradia - 7 years, 4 months ago

@Parth Viradia – Yup ;)

Kou$htav Chakrabarty - 7 years, 4 months ago

@Soaham Ganguly – I did the regression analysis and came up with answer 35 and I was disappointed.

Ashish Singh - 7 years, 4 months ago

Mark the blue point at the top left as 'A' and the blue point at the bottom right as 'B'...Then take the radius in a rounder as 'AB' and mark arcs at the top by keeping the point at 'A' and 'B' respectively...obviously they will cross each other..name the intersected point as 'C'..keep the rounder on 'C' and take radius 'BC' and continue the arc...u will see that according to the given data the arc will not cross the 40 second mark and hence a 40 second time is not possible :D :)

Parth Viradia - 7 years, 4 months ago

Pavel Verzhevsky
Jan 14, 2014

When x=1980, then y=49. When x=2010, then y=46. (46-49)/(2010-1980)=-3/30=-1/10 So, world record time decreases at a rate of 1 second for 10 years. Assuming further that the relationship between y and x will be linear, when x will be equal 2040, then y will be equal 43. Accordingly when x=2050, then y=42. The closest number to 42 of the responses is 43. Therefore, possible answer is 43, although I believe that the time a world record in 2050 will be about 42, and not 43 seconds.

Amitava M
Jan 13, 2014

By extrapolate the graph we can predict it easily.

I did the same. The beauty of more intuitive solutions is great.

Andrew Tiu - 7 years, 5 months ago

wat is extrapolate ???

viddhul tinku - 7 years, 4 months ago

extrapolating means extending the curve logically sometimes assuming curve is linear,parabolic etc

vijay katta - 7 years, 4 months ago

Raghav Dua
Jan 14, 2014

The graph has already crossed 55, so the fist option is logically out. From the graph, it is also evident that the latest record is pretty much already at 47. Assuming that this trend continues to reduce the time, 47 cannot be the answer as well. Now, if we analyze a bit more carefully from 1980 to 2020 (in 40 years), the speed has decreased by about 5 m/s. (assuming that by 2020, speed reaches 45). 35 seems an impossible choice since speed can't reduce by 10m/s by 2050 (In 30 years. And if we apply our brain power, we can reveal the truth that 30 is smaller than 40). Thus, 43 is logically the best answer

RedeXer Saeed
Feb 28, 2014

goood Question

Callum Farnden
Feb 14, 2014

Basically, you just have to read the graph off. You can use the multiple choice options to help. The trend is that record times are decreasing, and you therefore, rule out the two highest options. Then, by looking at the increase in the 40 years between 1970 and 2010, you can see it has dropped by about 5. However there is a slight curve on the graph - so 43 seems like a good answer. It may also help to print off the graph and draw a curve of best fit.

Bharath Bhat
Feb 1, 2014

form past few years, there isn't any drastic change in the timings of the champions but is greater 45 secs. so i the nearing future the bench mark would be close to 45 but will definitely be less than 45 secs. so it would be about 43 secs.

Harendra Pal Singh
Jan 14, 2014

In last 105 years run time was reduced by 18 sec, by unitary method we can calculate the run time reduction in 40 years, that is almost 7 sec. thus the time taken in 2050 might be 47 - 7 = 40 sec

Kalyan Pakala
Jan 13, 2014

The data is discrete and I chose to take a long interval for a linear pattern. From 1920 to 2020, the decrease is 62-47=15 (roughly). The percentage in decrease is 15%. For the next 30 years from 2020, the decrease would be 47-(15/100)* 30=4.5. Hence the best prediction would be 43 which is the nearest to 42.5!

I took the data from wikipedia and did some regression

exponential -> 1.81E4 * e^-2.97E-3 = 41.1 s

power -> y = 7.77E20 * x^-5.82 = 41.3 s

Antonio Valente Macarilay - 7 years, 4 months ago

Predicting The 2050 Olmypics Results

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