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 [tex]y=ab^{x}[/tex]
Putting the value of x in the above formula from 1st coordinate,
[tex]8.938=ab^{0}[/tex]
As [tex]b^{0}[/tex] = 1
this gives a= 8.938
Now using the 2nd coordinate
[tex]10.480=ab^{3}[/tex]
putting the value of a in it we have
[tex]10.480=8.938b^{3}[/tex]
taking cube roots on both sides we get
b= 1.05448
Now putting the values of a and b in the exponential formula-
[tex]y=8.938(1.05448)^{x}[/tex]
In the year 2028, x=28
so,
[tex]y=8.938(1.05448)^{28}[/tex]
y= 39.474
Hence oil consumption per day in 2028 will be 39.474 million barrels.
Answer:
Step-by-step explanation:
Let us assume 2010 to be year 0
The exponential function can be written as
[tex]P(t) = P_0 b^t[/tex], where t = no of years from 2010
Initial population P_0 = 8.938 million
In 2013, [tex]t=3[/tex]
Hence [tex]P(3) = 8.938 (b)^3=10.480\\b^3 = 1.173\\b = \sqrt[3]{1.173} =1.0545[/tex]
Hence [tex]P(t) = 8.938 (1.0548)^t[/tex]
Using this when t =28 we get as
[tex]P(28) = 8.938(1.0545)^28\\=39.4793[/tex] million
