1. **State the problem:** We want to find the average annual increase in world population between 1990 and 2010, given population data points for 1990, 2000, and 2010. 2. **Given data:** - Population in 1990: 5300 million - Population in 2000: 6100 million - Population in 2010: 6800 million 3. **Formula used:** To find the average increase per year, we use the formula for the slope of a line between two points: $$\text{Average increase per year} = \frac{\text{Change in population}}{\text{Change in years}}$$ 4. **Calculate the increase from 1990 to 2000:** $$6100 - 5300 = 800 \text{ million increase over } 10 \text{ years}$$ 5. **Calculate the increase from 2000 to 2010:** $$6800 - 6100 = 700 \text{ million increase over } 10 \text{ years}$$ 6. **Calculate the total increase from 1990 to 2010:** $$6800 - 5300 = 1500 \text{ million increase over } 20 \text{ years}$$ 7. **Calculate the average annual increase over 20 years:** $$\frac{1500}{20} = 75 \text{ million people per year}$$ 8. **Interpretation:** On average, the world population increased by about 75 million people each year between 1990 and 2010. **Final answer:** 75 million people per year.