Question

25. In 2004, a school population was 1250. By 2012 the population had dropped to 875. Assume the population is changing linearly. a How much did the population drop between the year 2004 and 2012? What is the average population decline per year? Find an equation for the population, P, of the school tyears after 2004.

Answer 1

To find the answers to your questions, we can use the concept of linear change.

1. How much did the population drop between the year 2004 and 2012?

To find the population drop, you can simply subtract the population in 2012 from the population in 2004:

Population in 2004 = 1250 Population in 2012 = 875

Population drop = Population in 2004 - Population in 2012 Population drop = 1250 - 875 Population drop = 375

So, the population dropped by 375 between 2004 and 2012.

2. What is the average population decline per year?

To find the average population decline per year, you can divide the total population drop by the number of years it took for the population to decline:

Number of years from 2004 to 2012 = 2012 - 2004 = 8 years

Average population decline per year = Population drop / Number of years Average population decline per year = 375 / 8 Average population decline per year = 46.875 (rounded to the nearest whole number, this would be approximately 47)

So, the average population decline per year is approximately 47.

3. Find an equation for the population, P, of the school t years after 2004.

Since the population is changing linearly, you can use the equation of a straight line, which is in the form of:

P(t) = mt + b

Where: P(t) = Population at time "t" years after 2004 m = Slope (average population decline per year) b = Initial population in 2004

We already calculated the average population decline per year (m) as approximately 47, and the initial population in 2004 (b) is 1250.

So, the equation for the population of the school t years after 2004 is:

P(t) = 47t + 1250

This equation will give you the population for any year after 2004 by plugging in the value of "t," which represents the number of years after 2004.