Pregunta
oflege Math (4246_5PH1)
WW 7 A
Question 5, 7.4.15
HW Score:
Points: 0 of 4
A countrys population and the growth rate in 2011 are given below. Ascume that the growth rate remains the same from year to year. Use this infomation and an exponentie to extimate the country’s population in the specilied year
pnopulation
(Round to the nearest hundredth as noeded)
WW 7 A
Question 5, 7.4.15
HW Score:
Points: 0 of 4
pnopulation
(Round to the nearest hundredth as noeded)
Ask by Hampton Bernard. in the United States
Mar 20,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The population in 2024 will be about 138.85 million.
Solución
Given:
- Initial population in 2011:
million - Annual growth rate:
which in decimal form is - Number of years from 2011 to 2024:
We use the exponential growth (decay) model:
Substitute the known values:
First, compute the annual multiplier:
Then raise it to the power of 13:
Calculating the exponent:
Thus:
Now compute the estimated population:
The population in 2024 is approximately
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Simplifique esta solución Beyond the Answer
To estimate the population in 2024 using an exponential growth model, we start with the initial population formula:
Where:
-
is the initial population (145 million), -
is the growth rate (converted to decimal form, which is -0.0328), and -
is the number of years from the start year to 2024 (which is 2024 - 2011 = 13 years).
Plugging the values into the equation gives:
Calculating that will help you find the estimated population in 2024!
You might find it interesting that the concept of population modeling with exponential functions has historical roots in demography. Since the 18th century, mathematicians like Thomas Malthus discussed population dynamics, and their ideas laid the groundwork for modern population studies. The interplay of growth rates has become crucial in planning for everything from city development to resource management!
In real-world applications, understanding population growth is essential for governments and organizations. For instance, countries use population projections to design infrastructure, healthcare systems, and educational services. Knowing the trends helps allocate resources where they’re needed most, ensuring that growing populations are well-supported and sustainable!
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