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.

1 answer

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.