In 2007, the population of a town was approximately 35,250. In 2012, the population of the town had decreased to 28,200. Based on a linear model, what will be the approximate population of the town in 2014?

Ive gotten -7050/2005= -4(rounded)
then for the answer i got 36228 people but got it wrong please help.

since it is linear, find the slope of the two ordered pairs that you have:

assume 2007 ----> t = 0
then for 2012 , t = 5

slope = (28200 - 35250)/(5-0) = -1410
(interpretation: the town loses 1410 each year)

so using the point (0,35250)
the equation can be written as
P = -1410t + 35250

so for 2014, t = 7
P = -1410(7) + 35250 = 25380

Since the population is clearly decreasing , your answer of 36228, which was more than what we started with, should have appeared to be illogical to you.

Well, it seems like there's a misunderstanding here. I apologize for any confusion caused by my previous response. Let's work through this again.

To find the approximate population of the town in 2014 using a linear model, we need to assume a consistent rate of change from 2012 to 2014.

First, let's find the rate of change per year. From 2007 to 2012, the population decreased by 35,250 - 28,200 = 7,050 people over 5 years. The average annual decrease is 7,050 / 5 = 1,410 people per year.

Now, we can estimate the population in 2014 by considering another two-year time interval. If the average annual decrease is 1,410 people, then over two years, the estimated decrease would be 1,410 * 2 = 2,820 people.

To find the population in 2014, we subtract 2,820 from the population in 2012:
28,200 - 2,820 = 25,380.

So, based on this linear model, the approximate population of the town in 2014 would be approximately 25,380 people.

Hope this clears things up!

To find the approximate population of the town in 2014, we can use the linear model based on the given data points: the population in 2007 (35,250) and in 2012 (28,200).

First, let's calculate the rate of change in population per year:
(28,200 - 35,250) / (2012 - 2007) = -7050 / 5 = -1410

This means that the population has been decreasing by approximately 1,410 people per year.

Next, let's calculate the change in population from 2012 to 2014 (2 years):
Change in population = rate of change Ɨ number of years
Change in population = -1410 Ɨ 2 = -2820

Finally, we can estimate the population in 2014 by subtracting the change in population from 2012:
Population in 2014 = Population in 2012 - Change in population
Population in 2014 = 28,200 - 2820 = 25,380

Therefore, the approximate population of the town in 2014 is 25,380.

To find the approximate population of the town in 2014 based on the given linear model, we need to determine the rate of change (slope) and use it to predict the population.

First, let's calculate the rate of change:

Rate of change = (change in population) / (change in years)

Change in population = 28,200 - 35,250 = -7,050
Change in years = 2012 - 2007 = 5

Rate of change = -7,050 / 5 = -1,410

Now that we have the rate of change, we can use it to predict the population in 2014.

To do this, we can calculate the change in population from 2012 to 2014 and then add it to the population in 2012.

Change in years = 2014 - 2012 = 2

Change in population = Rate of change * Change in years = -1,410 * 2 = -2,820

Predicted population in 2014 = Population in 2012 + Change in population = 28,200 - 2,820 = 25,380

Therefore, based on the linear model, the approximate population of the town in 2014 would be 25,380.