A towns population has been decreasing at a constant rate. In 2010 the population was 6,400. By 2012 the population dropped to 6,200. Assume the trend continues. Predict the population in 2016.
We can approach this problem by finding the rate of decrease per year and then using it to find the population in 2016.
First, we need to find the total decrease in population from 2010 to 2012:
6,400 - 6,200 = 200
The decrease occurred over two years, so the annual rate of decrease is:
200/2 = 100 people per year
Now we can use this rate to predict the population in 2016. We need to subtract the number of people by which the population decreased from 2012 to 2016, which is 4 x 100 = 400 people.
So the predicted population in 2016 is:
6,200 - 400 = 5,800
Therefore, the predicted population in 2016 is 5,800 people.
let t be the years after 2010
I treated it as two ordered pairs:
(0,6400) and (2,6200)
slope = (6200-6400)/2 = - 100
pop = -100t + 6400
so in 2016, t = 6
population in 2016 = -100(6) + 6400 = 5800