This project serves to examine the hypothetical effects of the implementation and repeal of China’s famous One Child Policy on the rate of population growth in that country through the use and applications of the basic exponential growth model. Calculates growth in three different scenarios and estmates the population for China in the year 2045

Gancarz, Greg

English

SPARK: Scholarship at Parkland | Parkland College

Parkland College
A with Honors Projects Honors Program
2017
Using the Pert Exponential Growth Model:
Predicting Past and Future Chinese Populations
Involving their Famous Population Control Policies
Greg Gancarz
Parkland College
Open access to this Essay is brought to you by Parkland College's institutional repository, SPARK: Scholarship at Parkland. For more information,
please contact spark@parkland.edu.
Recommended Citation
Gancarz, Greg, "Using the Pert Exponential Growth Model: Predicting Past and Future Chinese Populations Involving their Famous
Population Control Policies" (2017). A with Honors Projects. 208.
http://spark.parkland.edu/ah/208
Using the 𝑃𝑒𝑟𝑡 Exponential Growth Model  
Predicting past and future Chinese populations involving their famous population 
control policies 
Gregory Gancarz 
 
 This project serves to examine the hypothetical effects of the implementation and repeal 
of China’s famous One Child Policy on the rate of population growth in that country through the 
use and applications of the basic exponential growth model. Although the various contributing 
factors of Chinese population growth will be largely overlooked for the purposes of the 
scenarios, the main trends still present themselves quite accurately through its utilization. Three 
hypothetical trends regarding Chinese fertility rates will be examined and computed using the 
exponential growth equation:  
𝑃𝑒𝑟𝑡 
 
I. Effects on the Chinese population’s growth rate, had the One Child 
Policy and similar population control policies never been enacted and 
assuming all growth retardation was due to the policies’ effects. 
Up until the 1960’s the Chinese government encouraged families 
to birth as many children as possible. It wasn’t until the 60’s and 70’s that 
concerns regarding overpopulation began to arise and the government’s 
position completely reversed itself. By 1979, the One Child Policy had 
officially been implemented, but not before the government and concern 
over the cost of child rearing had already taken their toll on fertility rates. 
This example examines what the Chinese population would look like 
today had the government never switched its policy. It also assumes that 
all drop off in fertility rates would have been because of government 
interference and thus takes its population growth statistics from the years 
prior to when Chinese family-planning legislation took effect. This model 
also assumes all population growth would be able to be supported by the 
Chinese nation in regards to food and water and the other materials needed 
to prevent mass-starvation. 
 
For this equation, we need China’s population figures for 1955 and 1975, 598,574,241 and 
905,580,455 respectively, to plug them into the equation. The rate of time is 20 years. The only 
unknown variable is the rate: 
 
905,580,455 =  598,574,241𝑒20𝑟 
 
905,580,455
 598,574,241
= 𝑒20𝑟  
 
ln (
905,580,455
 598,574,241
) = 20r 
 ln (
905,580,455
 598,574,241
) ÷ 20 = r 
 
r = .02070 or 2.07% 
 
Now that we have the rate of growth in this 20 year period, we can use it to predict how large the 
population would have grown  if it were allowed to grow unfettered until recent years. For this 
equation, we simply plug the 1975 population in for p, and the rate of growth in for r. This 
growth model will take place over a period of 40 years, until 2015: 
 
905,580443𝑒(.0207)(40) 
= 
2,072,635,182 
 
So, assuming the growth rates prior to the change in population management policy continued 
unabated, China would now have a population of over two billion people, much more than the 
actual 2015 population: 1,376,048,943. 
 
II. Examining what China’s population level would be in 2045, assuming 
the repeal had never been enacted. 
In late 2015, the government of China announced that it would be 
ending its One Child Policy. A Two Child Policy would now be the 
standard to help combat an aging population. But what would the nation’s 
numbers look like if this never took place and the nation spent another 30 
years with the same method of population control? This scenario examines 
the possible growth effects. 
 
For this equation, we first need to calculate China’s growth rate under the One Child Policy. To 
calculate this, the population figures from 1980 and 2010 will be used; 977,837,433 and 
1,340,968,737 respectively 
 
1,340,968,737 =  977,837,433𝑒30𝑟 
. 
1,340,968,737
 977,837,433
= 𝑒30𝑟   
 
ln(
1,340,968,737
 977,837,433
) = 30r 
 ln(
1,340,968,737
 977,837,433
) ÷ 30 = r 
 
r = .0105 or 1.05% 
 
Now that the rate of growth is known, about 1.05%, we can apply it to a new equation 
calculating the population in 2045, using the 2010 population as the principal. Now that there are 
no undetermined variables, we simply plug in all the numbers. 
 
1,340,968,737𝑒 .0105(35) 
= 
1,936,519,502 
 
As we can see, if China never repealed their policy, the population would likely be just under 
two billion people in another three decades in 2045. Interestingly, even with an extra thirty years 
of growth, in 2045 the population under the control policies would still be less than what the 
unrestricted population would have been today, which was earlier calculated to have been just 
over two billion. 
 III. China’s population in 2045 with the new Two Child Policy being 
implemented. 
China has already seen the effects of over 30 years of one method 
of population control. Now how about three decades of another? This 
scenario examines what China’s population is likely to be under the Two 
Child Policy in another 30 years from now, using the little data that has 
currently been made available since the recent policy revision. 
 
For this equation we’ll be using China’s population in 2015, the year the policy was 
changed, and 2017, the most recently available population statistic we can use. 
 
1,388,232,693 =  1,376,048,943𝑒2𝑟 
 
1,388,232,693
 1,376,048,943
= 𝑒2𝑟   
 
ln(
1,388,232,693
 1,376,048,943
) = 2r 
 
ln(
1,388,232,693
 1,376,048,943
) ÷ 2 = r 
 
r = .00441 or .441% 
 
Surprisingly, the growth rate over the time period since the policy was changed would 
actually seem to be lower than the growth rate under the One Child Policy. This is a 
perfect example of the flaws of using such a broad, unprecise system to take averages, 
especially those of only two years. The lower growth rate calculated is a reflection of 
only a handful of numbers. While birth rates did fall immediately after the 
implementation of the One Child Policy, they dropped significantly lower in recent 
decades, from around 1.5% in the 1990’s to only about half a percent in the 2000’s. The 
large sample size taken for calculating the One Child Policy’s growth rate; from the 80’s 
until 2010, skewed the rate positively because it also included the relatively high growth 
rate of the 80’s and 90’s. The limited sample size of the Two Child Policy’s growth rate, 
on the other hand, only took the abysmal growth rates of 2015, 2016, and 2017 into 
account, all of which hovered around half a percentage point and were also below the 
government’s own expectations. 
As more time passes and more and more figures accumulate, it will likely become easier 
to paint a more accurate picture of what China’s future population will look like, unless 
the growth rate continues the trend of extremely low growth, despite the relaxed birth 
restrictions. Nevertheless, we will use the figures we have come up with now to estimate 
the 2045 population. 
 
1,388,232,693𝑒 .00441(28) 
= 
1,570,684,473 
 
And there we have it. Unless the growth rate defies predictions and remains at the current 
low levels, the 1.5 billion person estimate for 2045 is somewhat flawed, but as of now, 
it’s one of the best estimates we can glean, using this simple formula. 


Using the Pert Exponential Growth Model: Predicting Past and Future Chinese Populations Involving their Famous Population Control Policies

Scholarship at Parkland

Parkland CollegeA with Honors Projects Honors Program2017Using the Pert Exponential Growth Model:Predicting Past and Future Chinese PopulationsInvolving their Famous Population Control PoliciesGreg GancarzParkland CollegeOpen access to this Essay is brought to you by Parkland College's institutional repository, SPARK: Scholarship at Parkland. For more information,please contact spark@parkland.edu.Recommended CitationGancarz, Greg, "Using the Pert Exponential Growth Model: Predicting Past and Future Chinese Populations Involving their FamousPopulation Control Policies" (2017). A with Honors Projects. 208.http://spark.parkland.edu/ah/208Using the 𝑃𝑒𝑟𝑡 Exponential Growth Model  Predicting past and future Chinese populations involving their famous population control policies Gregory Gancarz   This project serves to examine the hypothetical effects of the implementation and repeal of China’s famous One Child Policy on the rate of population growth in that country through the use and applications of the basic exponential growth model. Although the various contributing factors of Chinese population growth will be largely overlooked for the purposes of the scenarios, the main trends still present themselves quite accurately through its utilization. Three hypothetical trends regarding Chinese fertility rates will be examined and computed using the exponential growth equation:  𝑃𝑒𝑟𝑡  I. Effects on the Chinese population’s growth rate, had the One Child Policy and similar population control policies never been enacted and assuming all growth retardation was due to the policies’ effects. Up until the 1960’s the Chinese government encouraged families to birth as many children as possible. It wasn’t until the 60’s and 70’s that concerns regarding overpopulation began to arise and the government’s position completely reversed itself. By 1979, the One Child Policy had officially been implemented, but not before the government and concern over the cost of child rearing had already taken their toll on fertility rates. This example examines what the Chinese population would look like today had the government never switched its policy. It also assumes that all drop off in fertility rates would have been because of government interference and thus takes its population growth statistics from the years prior to when Chinese family-planning legislation took effect. This model also assumes all population growth would be able to be supported by the Chinese nation in regards to food and water and the other materials needed to prevent mass-starvation.  For this equation, we need China’s population figures for 1955 and 1975, 598,574,241 and 905,580,455 respectively, to plug them into the equation. The rate of time is 20 years. The only unknown variable is the rate:  905,580,455 =  598,574,241𝑒20𝑟  905,580,455 598,574,241= 𝑒20𝑟   ln (905,580,455 598,574,241) = 20r  ln (905,580,455 598,574,241) ÷ 20 = r  r = .02070 or 2.07%  Now that we have the rate of growth in this 20 year period, we can use it to predict how large the population would have grown  if it were allowed to grow unfettered until recent years. For this equation, we simply plug the 1975 population in for p, and the rate of growth in for r. This growth model will take place over a period of 40 years, until 2015:  905,580443𝑒(.0207)(40) = 2,072,635,182  So, assuming the growth rates prior to the change in population management policy continued unabated, China would now have a population of over two billion people, much more than the actual 2015 population: 1,376,048,943.  II. Examining what China’s population level would be in 2045, assuming the repeal had never been enacted. In late 2015, the government of China announced that it would be ending its One Child Policy. A Two Child Policy would now be the standard to help combat an aging population. But what would the nation’s numbers look like if this never took place and the nation spent another 30 years with the same method of population control? This scenario examines the possible growth effects.  For this equation, we first need to calculate China’s growth rate under the One Child Policy. To calculate this, the population figures from 1980 and 2010 will be used; 977,837,433 and 1,340,968,737 respectively  1,340,968,737 =  977,837,433𝑒30𝑟 . 1,340,968,737 977,837,433= 𝑒30𝑟    ln(1,340,968,737 977,837,433) = 30r  ln(1,340,968,737 977,837,433) ÷ 30 = r  r = .0105 or 1.05%  Now that the rate of growth is known, about 1.05%, we can apply it to a new equation calculating the population in 2045, using the 2010 population as the principal. Now that there are no undetermined variables, we simply plug in all the numbers.  1,340,968,737𝑒 .0105(35) = 1,936,519,502  As we can see, if China never repealed their policy, the population would likely be just under two billion people in another three decades in 2045. Interestingly, even with an extra thirty years of growth, in 2045 the population under the control policies would still be less than what the unrestricted population would have been today, which was earlier calculated to have been just over two billion.  III. China’s population in 2045 with the new Two Child Policy being implemented. China has already seen the effects of over 30 years of one method of population control. Now how about three decades of another? This scenario examines what China’s population is likely to be under the Two Child Policy in another 30 years from now, using the little data that has currently been made available since the recent policy revision.  For this equation we’ll be using China’s population in 2015, the year the policy was changed, and 2017, the most recently available population statistic we can use.  1,388,232,693 =  1,376,048,943𝑒2𝑟  1,388,232,693 1,376,048,943= 𝑒2𝑟    ln(1,388,232,693 1,376,048,943) = 2r  ln(1,388,232,693 1,376,048,943) ÷ 2 = r  r = .00441 or .441%  Surprisingly, the growth rate over the time period since the policy was changed would actually seem to be lower than the growth rate under the One Child Policy. This is a perfect example of the flaws of using such a broad, unprecise system to take averages, especially those of only two years. The lower growth rate calculated is a reflection of only a handful of numbers. While birth rates did fall immediately after the implementation of the One Child Policy, they dropped significantly lower in recent decades, from around 1.5% in the 1990’s to only about half a percent in the 2000’s. The large sample size taken for calculating the One Child Policy’s growth rate; from the 80’s until 2010, skewed the rate positively because it also included the relatively high growth rate of the 80’s and 90’s. The limited sample size of the Two Child Policy’s growth rate, on the other hand, only took the abysmal growth rates of 2015, 2016, and 2017 into account, all of which hovered around half a percentage point and were also below the government’s own expectations. As more time passes and more and more figures accumulate, it will likely become easier to paint a more accurate picture of what China’s future population will look like, unless the growth rate continues the trend of extremely low growth, despite the relaxed birth restrictions. Nevertheless, we will use the figures we have come up with now to estimate the 2045 population.  1,388,232,693𝑒 .00441(28) = 1,570,684,473  And there we have it. Unless the growth rate defies predictions and remains at the current low levels, the 1.5 billion person estimate for 2045 is somewhat flawed, but as of now, it’s one of the best estimates we can glean, using this simple formula. 

https://spark.parkland.edu/cgi/viewcontent.cgi?article=1202&amp;context=ah

Using the Pert Exponential Growth Model: Predicting Past and Future Chinese Populations Involving their Famous Population Control Policies

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