The world is using more crude oil every year. In 2000 the world used about 76 million barrels a day and in 2010 the would be used about 87 million barrels a day. Assuming this is a linear trend come up with an equation for this. In addition, if consumption is not curved how many will we use in 2050? Can this trend be made less linear? Can it be flattened? Modeling this, what would it look like?

Answer:

Let the consumption of crude oil x years from 2000 be y million barrels per day.

We know that the point-slope form of the equation of a line passing through the points (x₁,y₁) and (x₂,y₂) is (y-y₁) = m(x-x₁) where m = (y₂-y₁)/(x₂-x₁).

Here, x₁ = 0, y₁ = 76, x₁ =10 and y₂= 87. Therefore, point-slope form of the equation of the line representing the given linear trend is (y-76)= [(87-76)/(10-0)](x-0) or, y-76 = 11x/10.

If the consumption is not curbed , the quantity of crude oil consumed in 2050 per day will be obtained by substituting x = 50 in the above equation.

Thus, the quantity of crude oil consumed in 2050 will be given by y-76 = 11*50/10 or, y = 76+ 55 = 131. Thus, the quantity of crude oil consumed in 2050 per day will be 131 million barrels.

There is nothing called less linear. A trend can either be linear or, non-linear.

However, this trend can be flattened by reducing m, i.e. the slope or, the rate of increase in the consumption of crude oil. For, example, if m gets reduced from 11/10 to 10/10 or, 1, the linear relationship will change to y-76 = x or, y = x +76. If m is reduced further to say 9/10, then the linear relationship will change to y-76 = 9x/10 or, y = 9x/10 +76.