Question: The table below shows the population of Manhattan for the years indicated, according to the
U.S. Census Bureau.
Year Population
1970 1,539,233
1980 1,428,285
1990 1,487,536
2000 1,537,195
2010 1,585,873
2020 1,643,734
Determine the average rate of change of the population per year between the years 1980 and
2020, rounded to the nearest integer.
1. **State the problem:** We need to find the average rate of change of Manhattan's population per year between the years $1980$ and $2020$.
2. **Formula for average rate of change:**
$$\text{Average rate of change} = \frac{\text{Change in population}}{\text{Change in time}} = \frac{P_{2020} - P_{1980}}{2020 - 1980}$$
3. **Identify values from the table:**
- Population in $1980$, $P_{1980} = 1,428,285$
- Population in $2020$, $P_{2020} = 1,643,734$
4. **Calculate the change in population:**
$$1,643,734 - 1,428,285 = 215,449$$
5. **Calculate the change in time:**
$$2020 - 1980 = 40$$
6. **Calculate the average rate of change:**
$$\frac{215,449}{40} = 5,386.225$$
7. **Round to the nearest integer:**
$$5,386$$
**Final answer:** The average rate of change of the population per year between $1980$ and $2020$ is approximately $5,386$ people per year.