Part I: Using the given data, follow the algorithm below to create a mathematical model which describes the population growth for the region. POPULATION 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 = 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 1990 4,740,318 2000 5,706,953 2010 6,800,180 2020 8,081,988 r = 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.
Part I: Using the given data, follow the algorithm below to create a mathematical model which describes the population growth for the region. POPULATION 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 = 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 1990 4,740,318 2000 5,706,953 2010 6,800,180 2020 8,081,988 r = 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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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Direction: Answer Part I and show complete and detailed solution (typewritten)
Transcribed Image Text:Part I: Using the given data, follow the algorithm below to create a mathematical model which describes the
population growth for the region.
1990
4,740,318
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
D1990-2000
R1990-2000
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
POPULATION
r =
2000
5,706,953
2010
6,800,180
2020
8,081,988
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:
Part II. Using a desmos, construct an exponential model that follows the form of either y = A(B)* or y = Aerx.
B. Exponential Model:
Part III. Use the two models (population growth model 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.
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Step 1: a) Find difference D in population
VIEWStep 2: b) Find the rate of growth R for each year interval
VIEWStep 3: c) Find the annual relative growth rate r
VIEWStep 4: d) Obtain the model for the population growth of your assigned model
VIEWStep 5: e) Estimate the population size of the regions in years 2030,2040 and 2050
VIEWStep 6: f) Find the year that population will reach 50 and 60 million
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