In 2014, a school population was 1320. By 2022 the population dropped to 840. Assume the population is changing linearly. By how many students did the population drop between 2014 and 2022?

Question

In 2014, a school population was 1320. By 2022 the population dropped to 840. Assume the population is changing linearly.

1. By how many students did the population drop between 2014 and 2022?
2. What is the mean population decline per year?
3. Find an equation for the population, P, of the school t years after 2014

Answer 1

1- If S(t) is the number of students in time, then S(2014) - S(2022) = 1340 - 840 = 480. Therefore the population has dropped by 480 students.

2- 2022 - 2014= 8 years, therefore: 480/8 = 60 is the mean decline. This means the slope of the line is -60.

3- If S(t)= a + b*t then from above we have b=-60. Therefore: S(t)= a - 60*b. Now if we plug in one of the points such as (2014,1340) in this line equation, we obtain: 1340 = a - 60*2014 and therefore a= 122160. The line equation will be: S(t)= 122160 - 60*t.