1. in what year did india (our second most populous country) begin to produce more energy than spain?
before 1997
in 2010
sometime in 2014
after 2016
question 2
which country was producing the most gigawatts of wind energy in 2000 at the beginning of the new century?
spain
united states
india
germany
question 3
which is true about the united states?
from 2009 to 2011, there was a plateau in energy creation, little new wind energy capacity was added.
in 2001, america was producing over 10 gw of wind energy.
from 1997 to 2000, america had as much wind energy capacity as germany.
in 2006, america was producing over 10 gw and began a steep climb in wind energy production.
question 4
what is the independent variable in this graph?
the given countries
years
gigawatts (gw)
wind energy capacity
both onshore and offshore wind so
question 5
what is the dependent variable in this graph?
the given countries
both onshore and offshore wind sources
years
gigawatts (gw)
wind energy capacity
question 6
what is the unit of the dependent variable?
gigawatts (gw)
the given countries
wind energy capacity
years
both onshore and offshore wind sources
question 7
what is a control (control variable) in this data?
the given countries
both onshore and offshore wind sources
gigawatts (gw)
years
wind energy capacity
question 8
in the middle of 2011, how much wind energy capacity was there in the united states? (interpolation).
55 gw
80 gw
65 gw
45 gw
question 9
how much wind energy capacity can india expect to have in 2020? (extrapolation)
30 gw
you should not guess and use only the data points that are given.
28 gw
36 gw
question 10
what is the general trend from 2009 to 2016 in the united states production of wind energy capacity? (slope).
additional 80 gw/year
addition 1 gw/year
additional 7 gw/year
additional 35 gw/year

Answers:

As we can see in the graph in 2014 there is an intersection between the lines that represent the wind energy production of Spain and India, then the production of India is increased, while that of Spain remains constant.

As we can see in the graph in 2000 Germany was the number 1 producer of gigawatts of wind energy. In addition it is observed a rapid growth and increase in production compared to the other countries.

In 1997, America began with a constant and very small energy production, which was growing gradually until 2006, when its rapid growth in production began to exceed the other countries shown in the graph.

When a function is plotted, generally the independent variable, whose value is previously set, is represented on the X axis.

In this sense, the variable found on the X axis of this graph is Years.

When a function is plotted, generally the dependent variable (which is generated from the independent variable) is represented on the Y axis.

In this sense, the variable found on the Y axis of this graph is Wind Energy Capacity.

We already know the dependent variable in this Wind Energy Capacity vs Years graph is Wind Energy Capacity, and its Unit is Gigawatts (GW).

Where

When we talk about scientific experimentation and representing data, the Control Variable is the one that remains constant (it does not change during the investigation).  

According to the explanation above, the option that fits with this characteristic is: Both onshore and offshore wind sources

If we want to make a linear interpolation to estimate how much wind energy capacity was there in the United States in the middle of 2011, firstly we need to find two points where the value we want to find is in the middle.

These points (X,Y) are:

P1: (2011,48) and P2: (2012,60)

Where X1:2011, Y1:48, X2:2012, Y2:60

Now we find the slope of the line with the following equation:

Then, with this value of the slope we can write the equation of the line and find the intersection point with one of the given points (we will use P1):

With this value and the slope, we can find Y for X=2011.5 (we need to know the wind capacity in the middle of 2011):

This is the estimated result 54 GW, and the option that is near this value is 55 GW

In this case we will apply a similar method as the previous answer, but estimating a prediction:

Let's find two points near the value we want to find. These points (X,Y) are:

P1: (2014,22) and P2: (2016,29)

Where X1:2014, Y1:22, X2:2016, Y2:29

Now we find the slope of the line with the following equation:

Then, with this value of the slope we can write the equation of the line and find the intersection point with one of the given points (we will use P2):

With this value and the slope, we can find Y for X=2020 (we need to estimate the expected wind capacity in 2020):

This is the estimated result 43 GW (note linear extrapolation is not as accurate as other methods), and the option that is near this value is 36 GW

In this case we will use the equation of the slope:

With the following points:

P1: (2009,35) and P2: (2016,82)

Therefore, the correct option is Additional 35 GW/Year

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .