Question

The U.S. Crude Oil production, in billions of barrels, for the years from 2015 projected to 2035, can be modeled y=−0.003x2+0.028x+1.995, with x equal to the years after 2015 and y equal to the number of billions of barrels of crude oil.a. Find and interpret the vertex of the graph of this model.b. What does the model predict the crude oil production will be in 2038?c. Graph the function for the years 2015 to 2035.

Answer 1

we have the equation

`y=-0.003x^2+0.028x+1.995`

this is the equation of a vertical parabola open downward

that means

the vertex is a maximum

using a graphing tool

see the attached figure

Part a

the vertex is the point (4.667, 2.06)

interpret the vertex

that means

For the year -----> 2015+4.665=2019.67=2020

the production is 2.06 billion of barrels of crude oil

Part b

What does the model predict the crude oil production will be in 2038​?

For x=2038-2015=23 years

substitute the value of x in the given equation

`y=-0.003(23)^2+0.028(23)+1.995`

y=1.052 billion of barrels of crude oil

Part c

Graph the function for the years 2015 to 2035

2015 ------> is For x=0

2035 ----> is For x=2035-2015=20

see the attached figure