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The problem provides the population of Palembang city modeled by the function:

\[
f(t) = 50.000 + 10.000 \cdot (t + 2)^2
\]

where \( t \) represents the number of years. The question asks for the estimated population in the very distant future.

### Solution:
In the long term, as \( t \to \infty \), the term \( (t + 2)^2 \) will dominate. Thus, the function can be approximated by:

\[
f(t) \approx 50.000 + 10.000 \cdot (t + 2)^2
\]

As \( t \) increases indefinitely, the \( (t + 2)^2 \) term becomes very large, meaning the population grows without bound. However, the problem likely implies that we are interested in understanding if there's any cap or if it simplifies in a more immediate sense.

Since this function continues to grow as \( t \to \infty \), and none of the provided answer choices (A to E) would match a population "in the distant future," it appears the problem may ask for the population estimate at some reasonable value of \( t \), or there is confusion in the framing.

Would you like further details on possible alternative interpretations, or clarification on one specific approach?

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### Follow-up Questions:
1. How does the parameter \( t \) influence the function?
2. What is the purpose of the constant term 50,000 in the function?
3. How does the population grow based on this model as \( t \) increases?
4. What is the significance of the \( (t+2)^2 \) term in relation to time?
5. How could we calculate the population for specific values of \( t \)?

### Tip:
As \( t \to \infty \), functions with quadratic terms grow rapidly, showing exponential-like behavior in long-term modeling.

Jumlah penduduk kota Palembang untuk t tahun ditaksir dan dinyatakan oleh fungsi berikut f(t) = 50.000 + 10.000 (t + 2)^2. Perkiraan jumlah penduduk dalam waktu yang sangat lama di masa yang akan datang adalah … jiwa.

Understand how to estimate the population of Palembang city using the quadratic growth model f(t) = 50,000 + 10,000 * (t + 2)^2. This problem explores key concepts of algebra and quadratic growth, suitable for students in Grades 9-12.

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