1. Introduction
After spending 30 years on the “endangered” list, China’s wild pandas have risen in numbers. Due to a population rise, panda nature reserves have grown from 40 to 67 since last surveyed. Traditional methods such as supporting the construction of roads and railroads, mining, deforestation, and poaching have steadied to a decline, resulting in an increase in the population of giant pandas. Legal protection and conservation efforts to protect habitations and forest farms were implemented by the Chinese government which was effectively introduced to lower extinction rates.
I chose this topic due to the recent news about the increase in the number of pandas. I have always loved pandas from a young age, and my interest in these furry friends cause me to wonder how abundantly they will continue to grow in the future. I decided to model exponential graphs showing the fluctuated population of wild pandas, along with the increase of wild pandas in the next 25, 50, 75 and 100 years to primarily show how improved wildlife conservation can help the increase of endangered species and prevent the extinction of animals essential to our world.
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2.1 Initial increase
Just in the last decade, giant panda populations have increased by almost 17%. The number of giant pandas globally have increased from 1,596 to 1,864 just from when they were last surveyed in 2003.
2.2 Census data
A problem I encountered while trying to research the panda population is it was very difficult to collect population records. I wondered if there was a way, I could collect credible sources showcasing panda populations. The solution I came up with was to compile research from multiple magazines and articles presenting populations of giant pandas in different time periods using the Official National Survey census from China. With this information, I created a data set as shown in Table 1.
Statistics of each Official National Survey
Official National Survey
Average Panda Population
- First National Survey (1971) 1,075
- Second National Survey (1987) 1,120
- Third National Survey (2003) 1,596
- Fourth National Survey (2019)Table 1: Panda populations according to each National Survey taken in China. 1,864
2.3 Exponential growth equation
To help visually aid this growth, an exponential equation and graph may be used. An ‘exponential’ equation is similar to that of a normal equation, however the variable, for example ‘x’, occurs in the exponent of the base.
An example of a basic equation is.
As you can see, the variable ‘x’ and ‘y’ is placed next to it’s respective coefficient, so when it is expanded, is ‘2 multiplied by ’ and is ‘6 multiplied by ’.
An exponential equation can be presented as shown in this example.
In this variable ‘x’ is shown as a power of it’s base which is 4. So if the exponential was to be expanded, it would be times until it equals 64.
An exponential equation can be used in real life situations such as to model populations, carbon date artifacts, for investments and to help determine time of death.
For example, the exponential growth formula can be used to create equations to determine population growth. In this equation ‘y’ is the future value, ‘ is the initial value, ‘r’ is the rate of growth as a percentage, and ‘t’ is the time intervals that have passed.
For example, a specific type of bacteria can double in just 15 minutes. At 10 am there are 1000 bacteria in the sample. How much bacterium will be present at 12 pm?
To calculate this, one must make an exponential equation using the formula.
So, ‘a’ will be 1000 because that is the initial value. The constant ‘r’ will be 100% as the population is doubling.
Lastly, ‘t’ is 2 since the growth is being calculated from 10 am to 12 pm, in 2 hours.
x 4
= 4000 bacterium were present at 12 pm.
Similarly, one can use this exponential growth formula to create an equation to estimate panda populations in the future.
Statistics of each Official National Survey
Official National Survey
Average Panda Population
- First National Survey (1971) 1,075
- Second National Survey (1987) 1,120
- Third National Survey (2003) 1,596
- Fourth National Survey (2019)Table 1: Panda populations according to each National Survey taken in China. 1,864
Using figure 1 one can also use the exponential growth formula to make an equation.
The initial value ‘a’ is 1075 so it can be substituted into ‘a’.
However, a problem I experienced when trying to construct this formula is that I didn’t know the current rate of growth. However, I found a formula that I could use to evaluate it.
Firstly, the most recent population of ‘1864’ and the initial value of ‘1075’ were substituted as ‘present’ and ‘ past’ values respectively.
Lastly, the number of years between 2019 and 1971 was 48, which was substituted into ‘n’.
This was simplified to get a growth rate of 0.011533 or approximately 1.2%.
If the growth rate is substituted into ‘r’, then the formula would be
Further simplified, the final formula is
I wasn’t sure if this was correct, and just to make sure I decided to use the ‘guess and check method to test.
I decided to substitute ‘48’ into ‘t’ years to see if it resulted in 1864 pandas.
x 1.73397
≈ 1864.02
But since it isn’t possible to have “0.02 of a panda”, the value is rounded down to 1864.
2.4 Constructing an exponential graph
If the equation that was made previously is used, it can help identify the rate of the population of pandas in the future when consistent conservation efforts are used. To show this, the initial value of “1864” must be used as the population of pandas in the future starts from the present time period. So, instead of ‘1075’ as the initial value as it was previous discussed, it would be changed to ‘1864’
So the formula will look like this:
The time in years is represented by ‘t’.
To show consistent time intervals, the time periods of increasing my 25 will be used (25, 50, 75, 100…). This means one must substitute each of these into the equation. For example, using this equation one could find the population of pandas as shown below.
Firstly 25 years would be substituted as a ‘t’ value.
x 1.33199
≈ 2482.83
≈ 2482 pandas
However, this value needs to be rounded down as it isn’t possible to have 0.83rd of a panda, thus resulting in an estimated population of 2482 giant pandas 25 years from now.
I continued to use this process to find values for population numbers 50, 75, and 100 years in the future. Once this was complete, I created a data set (Table 2) similar to Table 1.
Future panda populations
Year
Estimated populations of pandas
2044
2482
2069
3307
2094
4405
2119
5867
Figure 2: Estimated panda populations in the future based on the National Survey results.
2.5 Comparing methods of constructing an exponential graph
When I first tried to plot these points onto the graph, I had a problem where I wasn’t able to make it look like an exponential function. I used the points from table 2, but the points were simply by themselves and they didn’t look anything like a function, as shown in figure 1 below.
Future panda populations
Figure 1: When compared to the exponential function plotted on the graph, the points were nowhere near it and didn’t fit on the function.
Then I had realized this was the wrong method as just placing the points as they were wasn’t going to get me an exponential function. To make it into an exponential function, I would need to substitute values into the actual equation to find points that fit into the function.
So even though the first method didn’t work at all, it made me understand how to plot exponentials on graphs because they are different to standard expressions placed on graphs.
In the second method, the equation was placed into the graph, as shown in the exponential function in figure 2 below.
Future panda populations
Figure 2: The exponential function showing the possible increase of panda populations.
Then to show the increase in the next 25, 50, 75 and 100 years, the values from table 2 were plotted on the graph to show where they lie in the exponential function, as shown in figure 3.
Future panda populations
Figure 3: The left side shows the calculations, and the right side shows where each point is on the function.
The was when points were plotted on the function by writing the initial equation and substituting the ‘x’ for the number of years passed since the initial year ‘x’ as shown on the left side. The right side shows where the initial value and y-intercept which was (0,1864).
3. Conclusion
In conclusion, the aim was to model exponential graphs showing the initial increase of pandas and the significance of consistent wildlife conservation to show how panda populations will develop over time. Constructing an exponential equation from the current Official National Surveys of panda populations helped estimate populations in the next 25, 50, 75 and 100 years to show that if one makes an effort, there will be a positive response in caring for the environment. The final exponential graph showed a positive trend and significant increases in pandas after every 25 years. It has been a pleasant experience finding out that there can be a better future for the animals on our planet.
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