Cristiano Ronaldo's goals and the IRC

Introduction: Math can be related to anything even to soccer. Cristiano Ronaldo is considered one of the world's best soccer players. Ever since he started playing in Real Madrid more people have been looking at how many goals does he make each season. We will consider the amount of goals he has made per season ever since he got into Real Madrid FC in order to determine if his performance as a player has been improving per year. Real Madrid won this year the European Cup, so compare Ronaldo's performance in his second season in the club using the IRC to see if he is improving as a player

Season	Goals
2009-10	33
2010-11	53
2011-12	60
2012-13	55
2013-2014	51

Average Rate of Change:

(2, 53) to (3, 60) = 3-2/ 60-53 = 7

(2, 53) to (4, 55) = 4-2/ 55-53 = 1

(1, 33) to 2,53) = 2-1/ 53-33= 20

The calculations were done by using the slope of the line. If you pay attention you see that Ronaldo has been increasing his performance since the slopes are positives but that he has not been increasing the amount of goals per season.

Instantaneous Rate of Change:

We use the IRC to get closer and closer to a relationship we want to analyze. In this case Ronaldo's performance as a soccer player. It is done also by taking the slope of the points we want to analyze.

We calculate the IRC the following way:

(2, 53) to (3,45) 

We take the slope so: 3-2/ 45-53 = -8

(1, 15) to (2,53) 

We take the slope so: 2-1/ 53-15 = 38

We take the IRC by analyzing the two slope points we just calculated. Therefore we have

(-8+ 38) / 2 = 15

The 15 shows the IRC for Ronaldo during his second year as a player in Real Madrid. This shows that he has been improving from his first season to the next but taking into consideration that we had a negative slope of -8 in one of the points we must not overlook the fact that his goal average has been decreasing over the past years. Therefore even though Ronaldo did well in his second season and the ones that follow his increase in amount of goals may not seem so impressive when applying the IRC to be more specific.