The population of a city in 2005 was 18,000. By 2010, the city’s population had grown to 32,800. If the population growth follows a linear model, what is the projected population for 2015?
it grew (32,800 - 18,000) in five years
linear means the same amount of growth over the next five years
you have two ordered pairs, (2005,18000) and (2010,32800)
slope = (32800-18000)/(2010-2005)
= 14800/5 = 2960
so pop = 2960t + b, where t is the year
sub in one of the points, say (2005,18000)
18000 = 2960(2005) + b
b = -5916800
pop = 2960t - 5916800
replace t with 2015 to find pop
To find the projected population for 2015, we need to use the linear model that describes the population growth from 2005 to 2010.
First, we need to find the rate of population growth per year. We can do this by finding the difference in population between 2005 and 2010, and then dividing it by the number of years between these two points:
Population growth rate = (Population in 2010 - Population in 2005) / (Number of years between 2005 and 2010)
Population growth rate = (32,800 - 18,000) / (2010 - 2005) = 14,800 / 5 = 2,960
This means that the city's population increased by 2,960 people each year during this period.
Now, let's use this growth rate to project the population for 2015. To do this, we calculate the difference in years between 2015 and 2005, and then multiply it by the growth rate:
Difference in years = 2015 - 2005 = 10
Projected population for 2015 = Population in 2005 + (Difference in years * Population growth rate)
Projected population for 2015 = 18,000 + (10 * 2,960) = 18,000 + 29,600 = 47,600
Therefore, the projected population for 2015, assuming a linear growth model, is 47,600.