# Tigers' Weight vs Lions' Weight

### When Do They Weigh the Same? ~by AnudeepD

~ By AnudeepD- 536808

## What We Are Going to Examine

Siberian tigers and African lions are two of the largest big cats in the world, and Siberian tigers usually tend to be larger and heavier than lions, but is there a point in their lives when they are the same weight and the same age at the same time? This experiment aims to find out what point in their lives do tigers and lions(in zoos) weigh the same and at what age this happens. Linear growth rates of lions and tigers will be plotted on the same scatter plot and the point of intersection(solution to the linear system) will be found in order to answer our question of when do these two cats weigh the same.

## The Data

This is the data for the two cats.

## Notes

The lion data in blue is data that was hypothesized and placed on the graph based on what it should be(blue numbers). Not much lion data was collected because the graph would become too large. The lion growth data is too spread out, research found data about the weights of cubs at several different ages ranging from 12 days old to 7 weeks old to 5 months old.

## Refer to the Diagram Above

In order to come up with the hypothesized values, the difference between the two weight data points(4kg and 2.1kg) and was divided by the number of days taken to grow to that much, this gave the amount by which the lion's weight was increasing by. This value was then added to the initial weight(weight at birth because the new weight will be (rate at birth+weight change). Since, the values won't be exactly these values in the real world, they were lowered and increased by small amount.

For example, the 2.41kg data value was decreased to 2.3kg because in the real world, lions don't follow exact growth rates, the weight will always be off by a small amount. This was done for each hypothesized value.

## Process

Now the process in which this experiment was done will be discussed.

Step1) First, The data must be plotted and the line of best fit for the tiger data and lion data must be found. This line will show the trend in which the the tiger weight and lion weight is increasing by and should pass through most of the points. The lines of best fits, will help to find, approximately when lions and tigers weigh the same and have the same age.

Step2) Now the slope of each line must be found. The slope is basically the rate of change of the weight per day, or how many kg the animals are growing by everyday. This is done by finding two points on each line that have a whole number and exact coordinate (or most exact coordinate). We then find the difference between the weights given at each point and divide that by the difference between the days that each point represents. This will give is how many kg the animals grew by every day. In a mathematical sense, we are finding 2 coordinates on each line and finding the difference in y value(weight) and dividing it by the difference in x value(# of days).
Above

Data points for lion: (0days, 2.1kg) and (1day, ~2.25kg)

Data points for tiger: (0days, 0.68kg) and (2.5days, ~2.5kg)

Rate of Weight Change for Lion= (2.25kg-2.1kg) / (1day-0days)

= 0.15kg / 1 day

The rate of weight growth for African lion is 0.15kg per day.

Rate of Weight Change for Tiger= (2.5kg-0.68kg) / (2.5days-0days)

= (1.82kg) / (2.5days)

=0.728kg per day

The rate of weight growth for Siberian tiger is 0.768kg per day.

## The Equations

Now we can make the equations. The equations will be:

tiger's weight= (rate of weight change per day) X (# of days) + weight at birth

lion's weight= (rate of weight change per day) X (# of days) + weight at birth

Each animals weight is the rate of change at which the weight is increasing by daily, multiplied by the number of days that the animal has existed. This value is added to the weight at birth because animals' total weight is always how much it has grown so far+how much it weighed at first.

This can be seen mathematically as y=mx+b where y is the animal's total weight, m is the rate of growth, x is the number of days lived, and b is the weight at birth.

The equations for each animals are, officially:

Lion: W=0.15d+2.1 (W is dependent variable because it depends on d's value)

(d is independent variable)

W=total weight(kg)= y

d=# of days lived =x

0.15(kg)= growth rate per day =m

2.1(kg) = weight at birth =b

Tiger: W=0.728d+0.68 (W=dependent variable, d=independent variable)

W=total weight (kg)

d=# of days lived

0.728(kg)= growth rate per day

0.68(kg)= weight at birth

## The Final Graphs and Point of Intersection

Now Desmos will be used to draw the equations and finally find our point of intersection- our answer to when tiger and lion weight and age is the same.

## Significance of Solution, Discussion, Accuracy and Conclusion

We have found the point of intersection for both animals to be (2.298, 2.445). This means that African lion and Siberian tiger weight is the same at the same age of 2.298 or at approx. 2-3 days, when they are both 2.445kg heavy. Mathematically, the two lines representing the growth rates intersect at the point (2.298,2.445). This is the solution to this linear system. Also, it is important to note that before 2 days, African lion cubs tend to be heavier, but after 2 days, Siberian tigers tend to be heavier.

## Discussion

Although, to the normal person, this is not an extremely crucial piece of information to know, but there are many instances where a person may use this information. For example, if a biologist was studying African lions and Siberian tigers and needed test subjects that were the same weight and same age, then this data can help them find out what age lion and tiger they would need in order to have two subjects with the same weight and same age. Also, an average person who is curious about when a tiger and lion will weigh the same and have the same age will use this data. People might also use this information if they wanted to see which of the two animals will end up being bigger in the end. According to the graph, lions are heavier before the second day and tigers are heavier after the second day. On the second day(approximate), they weigh the same, as was discovered. Biologists in the future can even use this information to see how the growth rates of tigers and lions have changed over time.

## Accuracy

Although this find seems reasonable, there are a few inaccuracies in this conclusion. First of all, even though the growth rate of the tigers and lion is quite accurate, not every lion or tiger growth pattern will follow this graph. Each Siberian tiger and African lion is different, and so each animal has different growth patterns. Also, the lines representing this data is currently linear, but this data will not stay linear for too long because the weights of the animals can decrease and fluctuate at different times in their lives, and eventually they will stop growing. Also, this data was taken in a zoo, and tigers and lions in the wild will have different growth patterns as they are not fed everyday. Also, some of the lion data was hypothesized and wasn't experimentally collected, so that leads to a few inaccuracies.

However, this solution still does make sense because all the data was collected from reliable sources( zoo websites) and the lines of best fit have strong correlations. It is also sensible to think that African lions and Siberian tigers weigh the same when they are very young because these lions and tigers usually have a lot of difference in weight when they are older, but as cubs they are both small and are similar size and so they can have the same weight. Along with that, the graph shows that the Siberian tiger will end up being the bigger animal in the end which agrees with the true fact that Siberian tigers tend to be larger than African lions. On top of that, even though lions and tigers will stop growing at one point in their lives, when they are young, they are growing at a steady rate. This means that we are able to represent their growth as a linear relation. Also, this data represents the growth rates of African lions and Siberian tigers IN ZOOS, and in zoos these animals are fed everyday so it is logical to believe that they grow by significant amounts each day just as the graph shows.

## Conclusion

Therefore, African lions and Siberian tigers have the same weight and same age when they are 2.298 days old when they both weigh 2.445kg