Question

a citys population in the year $x = 1995$ was $y = 1,623,950$. in 1984 the population was 1,619,000. 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 450 people per year.
the population is increasing at a rate of 300 people per year.
the population is decreasing at a rate of 300 people per year.
the population is increasing at a rate of 400 people per year.
the population is decreasing at a rate of 400 people per year.
the population is increasing at a rate of 450 people per year.

Explanation:

Step1: Identify the two - point data

Let $(x_1,y_1)$ be the data for 1984 and $(x_2,y_2)$ be the data for 1995. So $x_1 = 1984$, $y_1=1619000$, $x_2 = 1995$, $y_2 = 1623950$.

Step2: Use the slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute the values: $m=\frac{1623950 - 1619000}{1995 - 1984}$.

Step3: Calculate the numerator and denominator

The numerator $1623950 - 1619000=4950$, and the denominator $1995 - 1984 = 11$.

Step4: Compute the slope

$m=\frac{4950}{11}=450$. Since the slope is positive, the population is increasing at a rate of 450 people per year.

Answer:

The population is increasing at a rate of 450 people per year.