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?
Please i need help with this i don't understand.
time starting at 2007
t n
0 35250
5 28200
7 ?
n = m t + 35250
28200 = m (5) + 35250
5 m = - 7050
m = -1410
so
n = -1410 t + 35250
if t = 7 years
n = -1410 (7) + 3520
To find the approximate population of the town in 2014 based on a linear model, we need to first determine the rate of change (slope) of the population over time.
To calculate the rate of change, we need to find the difference in population over the given time interval.
Change in population = Population in 2012 - Population in 2007
Change in population = 28,200 - 35,250 = -7,050
Next, we need to determine the number of years between 2007 and 2012, which is 5 years.
Using the rate of change, we can determine the average change in population per year:
Average Change in Population per year = Change in population / Number of years
Average Change in Population per year = -7,050 / 5 = -1,410
Therefore, the approximate population decrease is 1,410 people per year.
To find the approximate population in 2014, we can use the following formula:
Population in 2014 = Population in 2012 + (Average Change in Population per year * Number of years)
Population in 2014 = 28,200 + (-1,410 * 2)
Population in 2014 = 28,200 - 2,820
Population in 2014 = 25,380
Therefore, based on the linear model, the approximate population of the town in 2014 will be about 25,380.