This document presents a mathematical model for calculating population growth based on various factors. It develops three conjectures about the relationships between population growth and birth rates, death rates, and migration. The conjectures establish that population growth is directly proportional to birth rates and migration, but inversely proportional to death rates. The model is represented by the equation G = k * B - k' * D + k'' * M, where G is population growth rate and the other terms are constants multiplied by birth rate, death rate, and migration rate. The model provides a tool for accurately estimating population growth. It is recommended to continually refine the model by updating constant values and incorporating additional influencing factors.

1. SLIDESMANIA.COM
GOOD MORNING!

2. SLIDESMANIA.COM
KIZZ-MARK
PO-GRO’S
EQUATION

3. SLIDESMANIA.COM
PO-GRO’S
EQUATION OR
POPULATION
GROWTH EQUATION

4. SLIDESMANIA.COM
ABSTRACT:

5. SLIDESMANIA.COM
� Population growth is a critical phenomenon studied
in demography and other related fields. Mathematical
modeling offers a powerful approach to understanding
and predicting population dynamics. In this study, we
present a mathematical model for calculating population
growth based on various factors such as BIRTH
RATES, DEATH RATES, and MIGRATION.
Through this model, we aim to gain insights into
population trends, validate hypothesis, and provide
practical solutions for population analysis and
projection.

6. SLIDESMANIA.COM
INTRODUCTION:

7. SLIDESMANIA.COM
� Population growth plays a crucial role in societal
development and planning. Understanding the
factors influencing population growth is essential
for policymakers, urban planners, and researchers.
The Kizz-Mark Po-Gro’s Model aims to provide a
rigorous framework to analyze and quantify the
impact of various factors on population dynamics.
By formulating mathematical equations and
utilizing statistical techniques, we can estimate
population growth accurately and explore the
underlying mechanisms.

8. SLIDESMANIA.COM
CONJECTURES:

9. SLIDESMANIA.COM
CONJECTURE #1:
� Our first conjecture is centered around the relationship between birth
rates (B) and population growth. We hypothesize that population growth
can be calculated based on the number of births per unit of time. We
conjecture that the population growth rate (G) is proportional to the birth
rate:
Formula:
� G = k * B

10. SLIDESMANIA.COM
EXAMPLE:
Let’s consider a population with a birth rate of 100 births per year. Suppose after
analyzing historical data and applying statistical methods, we find that the value of k is
determined to be 0.02.
G = k * B
G = 0.02 * 100
G = 2
� Therefore, according to the conjecture, the population
growth rate would be 2 individuals per year based on a
birth rate of 100 births per year.
� Formula:
G = k * B,
where;
B =birth rate
k =constant of
proportionality.

11. SLIDESMANIA.COM
CONJECTURE #2
� Building upon the previous conjecture, we propose a
second conjecture regarding the influence of death rates (D)
on population growth. We conjecture that the population
growth rate is inversely proportional to the death rate:
� G = -k’ * D

12. SLIDESMANIA.COM
EXAMPLE:
� Let’s consider a population with a death rate of 50 deaths per year. Suppose
after analyzing historical data and applying statistical methods, we find that the
value of k’ is determined to be 0.01. Now we can calculate the population
growth rate.
G = -k’ * D
G = -0.01 * 50
G = -0.5
Therefore, the population growth rate would be -0.5 individuals per
year based on a death rate of 50 deaths per year. The negative sign
indicates a population decline due to the high death rate.
� Formula:
G = -k’ * D
where;
D = Death rate
-k’ =constant of
proportionality.

13. SLIDESMANIA.COM
CONJECTURE #3
� In addition to birth and death rates, our third conjecture
involves the effect of net migration (M) on population
growth. We hypothesize that population growth can be
modified by incorporating net migration:
Formula:
� G = k’’ * M

14. SLIDESMANIA.COM
EXAMPLE:
� Let’s consider a population with a net migration rate of 200 individuals per year. Suppose
after analyzing migration data and employing statistical methods, we find that the value of
k’’ is determined to be 0.03. Now we can calculate the population growth rate.
� Formula:
� G = k’’ * M
where;
M = net migration rate
k’’ = constant of
proportionality.
G = k’’ * M
G = 0.03 * 200
G = 6
� Therefore, according to the conjecture, the population growth rate
would be 6 individuals per year based on a net migration rate of 200
individuals per year. Positive net migration contributes to population
growth.

15. SLIDESMANIA.COM
Given a birth rate (B) of 20,000 per year, a death
rate (D) of 10,000 per year, and net migration
(M) of 5,000 per year, with constants of
proportionality k = 0.02, k’ = 0.01, and k’’ =
0.005, calculate the population growth rate (G).
EXAMPLE:
Formula:
G = k * B – k’ * D + k’’ * M

16. SLIDESMANIA.COM
G = (0.02 * 20,000) – (0.01 * 10,000) + (0.005 * 5,000)
G = 400 – 100 + 25
G = 325
Therefore, the population growth rate is estimated to be 325 individuals
per year.
SOLUTION:
Given:
k = 0.02 B = 20,000
k’ = 0.01 D = 10, 000
k’’ = 0.005 M = 5, 000

17. SLIDESMANIA.COM
Given a birth rate (B) of 15 per month, a death
rate (D) of 10 per month, and net migration (M)
of 5 per month, with constants of proportionality
k = 0.1, k’ = 0.05, and k’’ = 0.02, calculate the
population growth rate (G).
EXAMPLE:
Formula:
G = k * B – k’ * D + k’’ * M

18. SLIDESMANIA.COM
G = (0.1 * 15) – (0.05 * 10) + (0.02 * 5)
G = 1.5 – 0.5 + 0.1
G = 1.1
Therefore, the population growth rate is estimated to be 1.1 individuals
per month.
SOLUTION:
Given:
k = 0.1 B = 15
k’ = 0.05 D = 10
k’’ = 0.02 M = 5

19. SLIDESMANIA.COM
CONCLUSION:
In this study, we developed a mathematical
model for calculating population growth
based on birth rates, death rates, and net
migration. Through the analysis of historical
data and statistical techniques, we
established conjectures regarding the
relationship between these factors and
population growth. The model's formula, G
= k * B - k' * D + k'' * M, allows us to
estimate population growth rates accurately.
Our first conjecture suggests that population
growth is directly proportional to birth rates. By
determining the constant of proportionality (k)
through statistical analysis, we validated this
relationship. Similarly, our second conjecture
posits an inverse relationship between
population growth and death rates, which we
validated by finding the constant of
proportionality (k'). Lastly, our third conjecture
involves the impact of net migration on
population growth, showing a positive
relationship supported by the constant of
proportionality (k'').

20. SLIDESMANIA.COM
RECOMMENDATION:
The mathematical model presented in this study provides a valuable tool for policymakers, urban
planners, and researchers involved in population analysis and projection. By utilizing the formula G = k
* B - k' * D + k'' * M, population growth rates can be estimated based on birth rates, death rates, and net
migration.
� To further enhance the accuracy of the
model, it is recommended to continually
update and refine the values of the
constants of proportionality (k, k', k'')
based on the most recent data and
statistical analysis. This will ensure that
the model reflects the current
population dynamics accurately.
� Additionally, it is important to consider other
factors that may influence population growth,
such as socioeconomic factors, healthcare
advancements, and government policies.
Expanding the model to incorporate these
factors can provide a more comprehensive
understanding of population dynamics and
enable more accurate projections.

21. SLIDESMANIA.COM
RECOMMENDATION:
� Overall, the mathematical model presented in this study serves as a valuable
tool for population analysis and projection. By continuously refining and
expanding the model, policymakers and researchers can make informed
decisions and develop effective strategies to address the challenges and
opportunities associated with population growth

22. SLIDESMANIA.COM
Thank you!

23. SLIDESMANIA.COM
PRESENTED BY: