Question

A city's population in the year x=1980 was y=
1,629,800. In 1962 the population was 1,632,500.

Compute the slope of the population growth (or decline) and choose the most accurate statement from the following:
The population is decreasing at a rate of 300 people per year.
The population is increasing at a rate of 300 people per year.
The population is increasing at a rate of 50 people per year.
The population is decreasing at a rate of 50 people per year.
The population is decreasing at a rate of 150 people per year.
The population is increasing at a rate of 150 people per year.

Answer 1

To find the slope of the population growth (or decline) between the years 1962 and 1980, we first need to determine the change in population and the change in time.

1. **Population in 1962 (x = 1962)**: \(y_1 = 1,632,500\)
2. **Population in 1980 (x = 1980)**: \(y_2 = 1,629,800\)

Now, calculate the change in population (\(\Delta y\)) and the change in time (\(\Delta x\)):

\[
\Delta y = y_2 - y_1 = 1,629,800 - 1,632,500 = -2,700
\]

\[
\Delta x = 1980 - 1962 = 18
\]

Now, we can find the slope (rate of change):

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{-2,700}{18} = -150
\]

This means the population is decreasing by 150 people per year.

From the choices given, the most accurate statement is:

**The population is decreasing at a rate of 150 people per year.**