Questions: A city's population in the year x=1956 was y=3,424,500. In 1977 the population was 3,428,700. 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 100 people per year. The population is decreasing at a rate of 200 people per year. The population is decreasing at a rate of 400 people per year. The population is increasing at a rate of 400 people per year. The population is decreasing at a rate of 100 people per year. The population is increasing at a rate of 200 people per year.

A city's population in the year x=1956 was y=3,424,500. In 1977 the population was 3,428,700.

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 100 people per year. The population is decreasing at a rate of 200 people per year. The population is decreasing at a rate of 400 people per year. The population is increasing at a rate of 400 people per year. The population is decreasing at a rate of 100 people per year. The population is increasing at a rate of 200 people per year.
Transcript text: A city's population in the year $x=1956$ was $y=3,424,500$. In 1977 the population was 3,428,700. 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 100 people per year. The population is decreasing at a rate of 200 people per year. The population is decreasing at a rate of 400 people per year. The population is increasing at a rate of 400 people per year. The population is decreasing at a rate of 100 people per year. The population is increasing at a rate of 200 people per year. Question Help: Video Message instructor Add Work Calculator Submit Question Jump to Answer
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Solution

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Solution Steps

Step 1: Identify the given points

Given points are: \[ (x_1, y_1) = (1956, 3424500) \] \[ (x_2, y_2) = (1977, 3428700) \]

Step 2: Use the slope formula

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Step 3: Substitute the given values into the slope formula

\[ m = \frac{3428700 - 3424500}{1977 - 1956} \] \[ m = \frac{4200}{21} \] \[ m = 200 \]

Step 4: Interpret the slope

The slope \( m = 200 \) indicates that the population is increasing at a rate of 200 people per year.

Final Answer

The correct answer is A.

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