In 2012 a certain country recovered 24 of its municipal soli

In 2012, a certain country recovered 24% of its municipal solid wastes through recycling, up from 17% in 2007. Let P represent the percentage recycled and t the number of years since 2007. Find the linear equation for P as the function of t.

Solution

As per your question, there are two points having data:

Point-1 > 0 (for 2007 year) and 17 (percent recycled that year)
Point-2 > 5 (for 2012 year) and 24 (percent recycled that year)

Now let Point-1 and Point-2 have following co-ordinates respectively -

x1=0, y1=17
x2=5, y2=24

Now find the slope of the line joining these two points by using the formula
slope (m) = (y2-y1)/(x2-x1)
which gives m = (24-17)/(5-0)
or m = 7/5

Next, we will find the equation of this line by using the point/slope formula of straight lines y - y1 = m(x-x1)
y - 17 = 7/5(x-0)
y = 7x/5 + 17

It is our linear equation which can be written in P and t as -

P = 7t/5 + 17         ANS.