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marcosrodriguez5304
05.03.2020 •
Mathematics
In a certain region, about 6% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban population moves into the city. In 2015, there were 10,000,000 residents in the city and 800,000 in the suburbs. Set up a difference equation that describes this situation, where Subscript[x, 0] is the initial population in 2015. Then estimate the populations in the city and in the suburbs two years later, in 2017.
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Ответ:
City @ 2017 = 8,920,800
Suburbs @ 2017 = 1, 897, 200
Step-by-step explanation:
Solution:
- Let p_c be the population in the city ( in a given year ) and p_s is the population in the suburbs ( in a given year ) . The first sentence tell us that populations p_c' and p_s' for next year would be:
0.94*p_c + 0.04*p_s = p_c'
0.06*p_c + 0.96*p_s = p_s'
- Assuming 6% moved while remaining 94% remained settled at the time of migrations.
- The matrix representation is as follows:
- In the sequence for where x_k denotes population of kth year and x_k+1 denotes population of x_k+1 year. We have:
- Let x_o be the populations defined given as 10,000,000 and 800,000 respectively for city and suburbs. We will have a population x_1 as a vector for year 2016 as follows:
- To get the population in year 2017 we will multiply the migration matrix to the population vector x_1 in 2016 to obtain x_2.
- Where,
- The population in 2017 x_2 would be:
Ответ:
The answer to your question is 1
Step-by-step explanation:
Data
lim x - x³ + x⁵
x⇒∞ 1 - x² + x⁴
Process
1.- Divide by the term with the highest exponent
lim x/x⁵ - x³/x⁵ + x⁵/x⁵
x⇒∞ 1/x⁴ - x²/x⁴ + x⁴/x⁴
2.- Simplify
lim 1/x⁴ - 1/x² + 1
x⇒∞ 1/x⁴ - 1/x² + 1
3.- Evaluate when x⇒ ∞
lim 0 - 0 + 1
x⇒∞ 0 - 0 + 1
4.- Simplify
lim 1 = 1
x⇒∞ 1
5.- Result
lim 1
x⇒∞