Question
A city's population in the year x=1969 was y=2,683,150. In 1986 the population was 2,690,800.
Compute the slope of the population growth (or decline) and choose the most accurate statement from the following:
The population is increasing at a rate of 650 people per year.
The population is increasing at a rate of 450 people per year.
The population is decreasing at a rate of 650 people per year.
The population is decreasing at a rate of 450 people per year.
The population is decreasing at a rate of 300 people per year.
The population is increasing at a rate of 300 people per year.
Compute the slope of the population growth (or decline) and choose the most accurate statement from the following:
The population is increasing at a rate of 650 people per year.
The population is increasing at a rate of 450 people per year.
The population is decreasing at a rate of 650 people per year.
The population is decreasing at a rate of 450 people per year.
The population is decreasing at a rate of 300 people per year.
The population is increasing at a rate of 300 people per year.
Answers
GPT-4o mini
To calculate the slope of the population growth (or decline), we will use the following formula for slope:
\[
\text{slope} = \frac{\text{change in population}}{\text{change in time}}
\]
Given:
- In 1969 (x = 1969), the population (y) = 2,683,150
- In 1986 (x = 1986), the population (y) = 2,690,800
First, we calculate the change in population:
\[
\text{change in population} = 2,690,800 - 2,683,150 = 7,650
\]
Next, we calculate the change in time:
\[
\text{change in time} = 1986 - 1969 = 17 \text{ years}
\]
Now, we compute the slope:
\[
\text{slope} = \frac{7,650}{17} \approx 450
\]
The positive slope indicates that the population is increasing. Therefore, the population is increasing at a rate of approximately **450 people per year**.
From the options provided, the most accurate statement is:
**The population is increasing at a rate of 450 people per year.**
\[
\text{slope} = \frac{\text{change in population}}{\text{change in time}}
\]
Given:
- In 1969 (x = 1969), the population (y) = 2,683,150
- In 1986 (x = 1986), the population (y) = 2,690,800
First, we calculate the change in population:
\[
\text{change in population} = 2,690,800 - 2,683,150 = 7,650
\]
Next, we calculate the change in time:
\[
\text{change in time} = 1986 - 1969 = 17 \text{ years}
\]
Now, we compute the slope:
\[
\text{slope} = \frac{7,650}{17} \approx 450
\]
The positive slope indicates that the population is increasing. Therefore, the population is increasing at a rate of approximately **450 people per year**.
From the options provided, the most accurate statement is:
**The population is increasing at a rate of 450 people per year.**