The population of Linterhast was 3,600 people in 1990 and 4,800 people in 1993. If the population growth rate per 1,000 people is constant, what will the population be in 1996? A. 6,000 B. 6,400 C. 7,200 D. 8,000 E. 9,600

Let's assume that growth rate is X. We are told that per 1000 people the population is growing by X. That can be translated as X/1000. After 3 years, this should be (X/1000)^3. (x/1000)^3 * 3600 = 4800 -> (x/1000)^3 = 48/36 = 4/3 We can get (x/1000)^6 by squaring both sides (the question is asking what the population will be after 6 years). -> (x/1000)^6 = 16/9 -> 16/9 * 3600 = 6400

I think this is a high-quality question and I agree with explanation.

FYI, Differences Between Linear, Exponential, and Geometric Growth: Linear Growth : The population increases by a fixed amount each period (e.g., 400 people per year). The growth rate is constant in terms of the number of people added each period. Exponential Growth : The population increases by a fixed percentage of the current population each period. The growth rate is applied continuously, meaning each new increase depends on the most recent population size. The growth rate is often modeled with a continuous function (e.g., using erte^{rt}ert). Geometric Progression : The population increases by a fixed multiplicative factor (ratio) each period. The growth is discrete, and we apply the same ratio to the population for each time period, rather than continuously compounding it as in exponential growth. The main difference from exponential growth is that the population increases by a constant ratio in specific time periods (like yearly) rather than continuously.

I like the solution - it’s helpful.

I figured the meaning of ques as growth rate is constant every 1000 ppl, so the change of 1200 in the first 3 years is being by 200 so for the 3 years the diff should again come from after 4800--5800 (constant) and 200 was in the first 3 years so it should be slightly more than 200 for the next 3 years and so on. Can you please tell me if this approach was correct and give me a fundamental understanding of this approach as if its correct, I feel it's partial in nature?

Your interpretation is a common misunderstanding. Let’s break it down. The phrase “population growth rate per 1,000 people is constant” means the population grows by a constant percentage , not by a fixed number of people each time. From 1990 (3,600) to 1993 (4,800), the population grew by 1,200. But notice that 1,200 is not the important part, the ratio is: 4,800/3,600 = 4/3. That means over 3 years, the population multiplied by 4/3 (≈ 1.3...). If the growth were a constant number (like 200 per 1,000 every 3 years), then the increase in raw numbers would be the same each cycle. But here the increase is proportional to the size of the population. That’s why after 1993 the population grows faster in absolute terms: 1990–1993 increase: 1,200. 1993–1996 increase: 1,600 (to 6,400). So your “fixed increase” idea is only partially right, it matches the first cycle but doesn’t capture the compounding effect of percentage growth. That’s why the fundamental method is: Population in 1996 = 4,800 * 4/3 = 6,400. Hope it's clear.