Question

For the following exercise, consider this scenario: A town's population has been increasing at a constant rate. In 2010 the population was 45000 . By 2012 the population had increased to 51250 . Assume this trend continues linearly. Predict the population in 2016.

Answer 1

Answer:

63,750

Step-by-step explanation:

#Calculate the rate of change per year:

$\bigtriangleup=\frac{2012 \ pop- 2010\ pop}{2012-2010}\\\\=\frac{51250-4500}{2}\\\\=3125$

The population increasing by a constant of 3125 per year.

-Let x be the time in years

-The general form of a linear equation is

$y=mx+c, c=45000\\\\\therefore y=mx\\\\y(x)=3125x+45000$

The population in 2016 is therefore predicted as:

$y=mx+c\\\\y(2016-2010)=3125x+45000\\\\y(6)=3125\times 6+45000\\\\=63750$

Hence, the population in 2016 is 63,750