I can not make sense of this, can anyone help me?

Question

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 1

In 2000: 76 mil. -> (0,76) the measured amount at time zero

In 2010: 87 mil. -> (10,87) the measured amount ten years later

Using these 2 points, find the slope... m = 11/10

Plug the slope and either point (I chose the first) into the point-slope form of the equation of a line:

y - 76 = 11/10(x - 0) --> y = 11x/10 + 76

For 2050: How many million barrels? --> (50, ?) We have x but need y. Use the equation we've just derived:

y = 11(50)/10 + 76 = 131

So, with the same usage every year [that's what makes/keeps it linear], in 2050 the usage would be

131 million barrels.

I don't know what "less linear" means, but to be non-linear would each year usage is changing by a different amount.

To "flatten" I guess, would mean to not change from one year to the next [slope = 0].

Modeling this would mean just that--not change usage amount from one year to the next.