1. **State the problem:** A city starts with a population of 62,000 and after 25 years, the population is 78,000. We need to find how much the population increases each year. 2. **Formula used:** The population increase per year can be found using the formula for average rate of change: $$\text{Increase per year} = \frac{\text{Final population} - \text{Initial population}}{\text{Number of years}}$$ 3. **Apply the values:** $$\text{Increase per year} = \frac{78,000 - 62,000}{25}$$ 4. **Calculate the difference:** $$78,000 - 62,000 = 16,000$$ 5. **Substitute back:** $$\text{Increase per year} = \frac{16,000}{25}$$ 6. **Simplify the fraction:** $$\frac{16,000}{25} = \frac{\cancel{16,000}}{\cancel{25}} = 640$$ 7. **Interpretation:** The population increases by 640 people each year on average. **Final answer:** The population increases by **640** people per year.