Question

A city's population in the year 2 = 1952 was y = 2,933,200. In 1958 the population was 2,932,300.Compute the slope of the population growth (or decline) and choose the most accurate statementfrom the following:O The population is increasing at a rate of 150 people per year.O The population is decreasing at a rate of 150 people per year,O The population is decreasing at a rate of 50 people per year.The population is increasing at a rate of 50 people per year.The population is increasing at a rate of 250 people per year.The population is decreasing at a rate of 250 people per year.Question Help: D Video Message instructorSubmit QuestionJump to Answer

Answer 1

You have the following populations in two different years:

year 1952 -> population = 2,933,200

year 1958 -> population = 2,932,300

The previous information can be considered as a pair of points in the coordinate plase, in which you have a function that determines the population dependeing of the year.

To know the rate of increasing or decreasing of the population, you calculate the slope of the fuction. You use the following formula:

m = (y2 - y1)/(x2 - x1)

(x1,y1) and (x2,y2) are two points of the function. In this case you can take (x1,y1) = (1952, 2,933,200) and (x2,y2) = (1958, 2,932,300). By replacing in the formula for the slope m youhave:

m = (2,932,300 - 2,933,200)/(1958 - 1952)

m = -900/6 = -150

Then, the slope of the function is -150. This means that the population is decreasing (minus sign) at a rate of 150 people per year.