Sure, let's break down the problem step-by-step:
1. Current population of the city:
- The city currently has 38,000 residents.
2. New residents added each year:
- The city adds 1,500 new residents each year.
3. Time period:
- We are considering a period of 9 years.
4. Calculate the total number of new residents added over 9 years:
- Each year 1,500 new residents are added.
- Over 9 years, the total number of new residents added is [tex]\( 1,500 \times 9 = 13,500 \)[/tex].
5. Calculate the total population after 9 years without considering the remaining proportion:
- Initial population: 38,000
- Number of new residents added in 9 years: 13,500
- Total population after 9 years: [tex]\( 38,000 + 13,500 = 51,500 \)[/tex].
6. Determine the proportion of residents remaining after 9 years:
- The proportion of residents remaining after [tex]\( t \)[/tex] years is given by the formula [tex]\( S(t) = \frac{1}{t+1} \)[/tex].
- For [tex]\( t = 9 \)[/tex]: [tex]\( S(9) = \frac{1}{9+1} = \frac{1}{10} = 0.1 \)[/tex].
7. Calculate the final population considering the remaining proportion:
- The total population without considering the proportion after 9 years is 51,500.
- The proportion of remaining residents is 0.1.
- Therefore, the final population after 9 years is [tex]\( 51,500 \times 0.1 = 5,150 \)[/tex].
8. Round the final population to the nearest integer:
- The final population is approximately 5,150 residents.
So, the population of the city nine years from now is approximately 5,150 residents.
