Direction: Show your complete and detailed solution in Part II. (I attached the Part I for the overview of the continous exponential model) Part II. Using a computer graphing calculator software (state what did you use), construct an exponentialmodel that follows the form of either y = A(B)* or y = Aex. Use the two models (continuous exponentialand exponential model) to estimate the population size of the region assigned to you in years 2030, 2040,and 2050. Show only the whole number part of the resultREGIONCentral Visayas19904,740,318POPULATION20005,706,95320106,800,18020208,081,988 Part I: Using the given data, follow the algorithm below to create a mathematical model which describes thepopulation growth for the region.REGIONCentral Visayasa) Compute the difference D in population during the following year intervals: 1990-2000; 2000-2010: and 2010-2020.b)Use the formula below to get the rate of growth R of each year interval: Let R1990-2000 be therelative growth rate of the 1990-2000 year interval. Its formula is defined asR1990-2000 =19904,740,318POPULATION1 =20005,706,95320106,800,18020208,081,988D1990-2000P2000where D1990-2000 is the difference of the population in 1990 and 2000; and P1990 is the populationin 1990. (Express answers in this part in four decimal places).c) Find the average (arithmetic mean) of the three rates then divide it by 10. The result will serve asthe annual relative growth rate r of the region's population. Express this in four decimal places.R1990-2000 + R2000-2010 + R2010-2020310d)Let t=0 be year 1990, prepare the model for the population growth of your assigned region usingthe continuous exponential model C(t) = Poet.e) Use answer in letter d to estimate the population size of the region in years 2030, 2040, and 2050.Show only the whole number part of the result.f)Using the same model, estimate the year in which the population will reach the 50 and 60 millionmilestone. Show only the whole number part of the result.A. Population Growth Model:

Given the data of population growth of a region. It is required to find the model for the population…

Part II. Using a computer graphing calculator software (state what did you use), construct an exponential model that follows the form of either y = A(B)* or y = Ae*. Use the two models (continuous exponential and exponential model) to estimate the population size of the region assigned to you in years 2030, 2040, and 2050. Show only the whole number part of the result REGION Central Visayas 1990 4,740,318 POPULATION 2000 5,706,953 2010 6,800,180 2020 8,081,988

Part II. Using a computer graphing calculator software (state what did you use), construct an exponential model that follows the form of either y = A(B)* or y = Ae*. Use the two models (continuous exponential and exponential model) to estimate the population size of the region assigned to you in years 2030, 2040, and 2050. Show only the whole number part of the result REGION Central Visayas 1990 4,740,318 POPULATION 2000 5,706,953 2010 6,800,180 2020 8,081,988

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Direction: Show your complete and detailed solution in Part II. (I attached the Part I for the overview of the continous exponential model)

Part II. Using a computer graphing calculator software (state what did you use), construct an exponential
model that follows the form of either y = A(B)* or y = Aex. Use the two models (continuous exponential
and exponential model) to estimate the population size of the region assigned to you in years 2030, 2040,
and 2050. Show only the whole number part of the result
REGION
Central Visayas
1990
4,740,318
POPULATION
2000
5,706,953
2010
6,800,180
2020
8,081,988

Part I: Using the given data, follow the algorithm below to create a mathematical model which describes the
population growth for the region.
REGION
Central Visayas
a) Compute the difference D in population during the following year intervals: 1990-2000; 2000-
2010: and 2010-2020.
b)
Use the formula below to get the rate of growth R of each year interval: Let R1990-2000 be the
relative growth rate of the 1990-2000 year interval. Its formula is defined as
R1990-2000 =
1990
4,740,318
POPULATION
1 =
2000
5,706,953
2010
6,800,180
2020
8,081,988
D1990-2000
P2000
where D1990-2000 is the difference of the population in 1990 and 2000; and P1990 is the population
in 1990. (Express answers in this part in four decimal places).
c) Find the average (arithmetic mean) of the three rates then divide it by 10. The result will serve as
the annual relative growth rate r of the region's population. Express this in four decimal places.
R1990-2000 + R2000-2010 + R2010-2020
3
10
d)
Let t=0 be year 1990, prepare the model for the population growth of your assigned region using
the continuous exponential model C(t) = Poet.
e) Use answer in letter d to estimate the population size of the region in years 2030, 2040, and 2050.
Show only the whole number part of the result.
f)
Using the same model, estimate the year in which the population will reach the 50 and 60 million
milestone. Show only the whole number part of the result.
A. Population Growth Model:

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Step 2: Obtain the model for the population growth of exponential model using calculator

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Step 3: Estimate the population size of the regions in years 2030,2040 and 2050 (graphic calculator)

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Step 4: Obtain the model for the population growth of continuous exponential model (as in d of part I)

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Step 5: Estimate the population size of the regions in years 2030,2040 and 2050 using model of d in part I

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