The population of a town was 3600 three years ago and is 4800 at present. Assuming that the population has been growing at a constant rate compounded annually, what will be the population of the town three years from now?

Introduction:
This problem uses the concept of compound growth, commonly applied to population growth, investment growth and similar situations. You are given the population at two times separated by three years and must project the population three years further into the future, assuming the same annual growth rate continues.

Given Data / Assumptions:

• Population 3 years ago (P0) = 3600.
• Population now (after 3 years) = 4800.
• Growth rate is constant and compounded annually.
• We need the population 3 years from now, that is, 6 years after the base time P0.

Concept / Approach:
Let the annual growth factor be k = (1 + r), where r is the annual growth rate in decimal form. Then population after 3 years is P0 * k^3 and after 6 years is P0 * k^6. Given P0 * k^3 = 4800 and P0 = 3600, we can find k^3, and then k^6. Using k^6, we find the population after 6 years, which is 3 years from now.

Step-by-Step Solution:
Let P0 = 3600 and let k be the annual growth factor.After 3 years: P0 * k^3 = 4800So 3600 * k^3 = 4800Thus k^3 = 4800 / 3600 = 4/3Now, after 6 years (3 more years from now): population = P0 * k^6But k^6 = (k^3)^2 = (4/3)^2 = 16/9Therefore, population after 6 years = 3600 * 16/93600 / 9 = 400, so population = 400 * 16 = 6400

Verification / Alternative Check:
You can think of it another way: from 3 years ago to now, population multiplied by 4/3. Assuming the same growth, over the next 3 years it again multiplies by 4/3. Hence future population = 4800 * 4/3 = 4800 * 1.333... = 6400, which agrees with the previous method.

Why Other Options Are Wrong:
6000 and 6500: These values do not correspond to the same compound growth factor that took the population from 3600 to 4800.6600 and 7200: Both are larger than the correctly computed value and are inconsistent with the implied annual growth rate.

Common Pitfalls:
Some students mistakenly treat the growth as linear and add the same absolute increase (for example, adding 1200 every three years) instead of compounding. Others compute the annual rate and then misapply it over the subsequent 3 years. Using the k^3 and k^6 approach helps keep the computation clean and avoids rate rounding errors.

Final Answer:
The population of the town three years from now will be 6400.