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Sagot :
(a) To find the initial population [tex]\( P \)[/tex] given the population after [tex]\( T \)[/tex] years, denoted as [tex]\( P_T \)[/tex], and the growth rate [tex]\( R \)[/tex], the formula used is:
[tex]\[ P = \frac{P_T}{(1 + \frac{R}{100})^T} \][/tex]
This formula accounts for compound growth over [tex]\( T \)[/tex] years.
(b) The population after 2 years ([tex]\( P_T \)[/tex]) is given as 30000. This includes 5800 people who migrated into the town.
So, the population due to natural growth, excluding migration, is:
[tex]\[ \text{Population excluding migration} = 30000 - 5800 = 24200 \][/tex]
(c) Now, to find the initial population [tex]\( P \)[/tex] before 2 years, we rearrange the formula:
[tex]\[ P = \frac{24200}{(1 + \frac{10}{100})^2} \][/tex]
Calculating this using the given data:
[tex]\[ P = \frac{24200}{(1 + 0.10)^2} \][/tex]
[tex]\[ P = \frac{24200}{1.21} \approx 20000 \][/tex]
So, the initial population before 2 years was approximately 20000.
[tex]\[ P = \frac{P_T}{(1 + \frac{R}{100})^T} \][/tex]
This formula accounts for compound growth over [tex]\( T \)[/tex] years.
(b) The population after 2 years ([tex]\( P_T \)[/tex]) is given as 30000. This includes 5800 people who migrated into the town.
So, the population due to natural growth, excluding migration, is:
[tex]\[ \text{Population excluding migration} = 30000 - 5800 = 24200 \][/tex]
(c) Now, to find the initial population [tex]\( P \)[/tex] before 2 years, we rearrange the formula:
[tex]\[ P = \frac{24200}{(1 + \frac{10}{100})^2} \][/tex]
Calculating this using the given data:
[tex]\[ P = \frac{24200}{(1 + 0.10)^2} \][/tex]
[tex]\[ P = \frac{24200}{1.21} \approx 20000 \][/tex]
So, the initial population before 2 years was approximately 20000.
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