Question

Oil consumption in China grew exponentially from 8.938 million barrels per day in 2010 to 10.480 million barrels per day in 2013. Assuming exponential growth continues at the same rate, what will oil consumption be in 2028?

Round your answer to three decimal places.

Oil consumption will be approximately ___ million barrels per day in 2028.

Answer 1

Explanation:

Let us assume 2010 to be year 0

The exponential function can be written as

`P(t) = P_0 b^t`, where t = no of years from 2010

Initial population P_0 = 8.938 million

In 2013,
`t=3`

Hence
`P(3) = 8.938 (b)^3=10.480\\b^3 = 1.173\\b = \sqrt[3]{1.173} =1.0545`

Hence
`P(t) = 8.938 (1.0548)^t`

Using this when t =28 we get as

`P(28) = 8.938(1.0545)^28\\=39.4793` million

Answer 2

Let the year represents x axis and consumption represents y axis.

Since 2010 is the initial year, x=0

and 2013 is third year , so x=3

Co-ordinates are (0,8.938)(3,10.480)

Exponential formula is
`y=ab^(x)`

Putting the value of x in the above formula from 1st coordinate,

`8.938=ab^(0)`

As
`b^(0)` = 1

this gives a= 8.938

Now using the 2nd coordinate

`10.480=ab^(3)`

putting the value of a in it we have

`10.480=8.938b^(3)`

taking cube roots on both sides we get

b= 1.05448

Now putting the values of a and b in the exponential formula-

`y=8.938(1.05448)^(x)`

In the year 2028, x=28

so,

`y=8.938(1.05448)^(28)`

y= 39.474

Hence oil consumption per day in 2028 will be 39.474 million barrels.