Question

A small rural town has experienced a population decrease at a rate of 25 people every 5 years since 1970. If the population of the town in 1970 was 250, which of the following equations represents the town’s population as a function of time? (Assume 1970 is represented by x = 0, 1971 is represented by x = 1, and so on).

Answer 1

Population decreases at the rate of 25 people every 5 years

slope of a line = difference in y / difference in x (or rise / run) = -25 / 5
slope m = -5

when x = 0 (that is the year 1970 ), the population is 250
x = 0 represents the y -intercept

So which answer choice has slope = -5 and y-intercept =250?


OR IF THAT WAS HARD TO UNDERSTAND

The initial population is 250
It decreases at a rate of 5 people per year

After year one, it will be 250 - 1(5)
After year two, it will be 250 - 2(5)
After year three, it will be 250 - 3(5)

After year x, it will be 250 - x(5)

The function is y = -5x + 250