Chapter 7.1, Problem 64E

a.

To determine

To analysis data on renewable energy.

Answer to Problem 64E

  $\boxed{y=0.157t^3-2.229t^2+12.494t+153.587}$

  $\boxed{y=13.63t^2-61.293t+150.595}$

Explanation of Solution

Given information:

The table shows the consumption $C$ (in trillions of Btus) of geothermal energy and wind energy in the United States from $2001$ through $2009$ .

  

  

Use a graphing utility to find a cubic model for the geothermal energy consumption data and a quadratic model for the wind energy consumption data. Let $t$ represent the year, with $t=1$ corresponding to $2001$ .

Calculation:

Enter the data in calculator.

Press the button STAT and select EDIT

Enter years in $L_1$ and geothermal consumption in $L_2$ .

Then cubic regression is $\boxed{y=0.157t^3-2.229t^2+12.494t+153.587}$

  

Enter year in $L_1$ and wind energy consumption in $L_2$ .

Then quadratic equation is $\boxed{y=13.63t^2-61.293t+150.595}$

  

b.

To determine

To analysis data on renewable energy.

Answer to Problem 64E

  

Explanation of Solution

Given information:

The table shows the consumption $C$ (in trillions of Btus) of geothermal energy and wind energy in the United States from $2001$ through $2009$ .

  

  

Use the graphing utility to graph the data and the two models in the same viewing window.

Calculation:

Enter the data in calculator.

Press the button STAT and select EDIT

Enter years in $L_1$ and geothermal consumption in $L_2$ .

Then cubic regression is $\boxed{y=0.157t^3-2.229t^2+12.494t+153.587}$

  

Enter year in $L_1$ and wind energy consumption in $L_2$ .

Then quadratic equation is $\boxed{y=13.63t^2-61.293t+150.595}$

  

Data and model are shown as,

  

c.

To determine

To analysis data on renewable energy.

Answer to Problem 64E

Two curves intercept at $\boxed{t=4.9}$

Explanation of Solution

Given information:

The table shows the consumption $C$ (in trillions of Btus) of geothermal energy and wind energy in the United States from $2001$ through $2009$ .

  

  

Use the graph from part $\left(b\right)$ to approximate the point of intersection of the graphs of the models. Interpret your answer in the context of the problem.

Calculation:

Data and model are shown as,

  

Two curves intercept at $\boxed{t=4.9}$

Both consumptions are equal in beginning of the year $\boxed{2005}$

d.

To determine

To analysis data on renewable energy.

Answer to Problem 64E

We cannot predict the wind energy in the future.

We can predict the geothermal consumption.

Explanation of Solution

Given information:

The table shows the consumption $C$ (in trillions of Btus) of geothermal energy and wind energy in the United States from $2001$ through $2009$ .

  

  

Describe the behaviour of each model. Do you think the models can accurately predict consumption of geothermal energy and wind energy in the United States for future years? Explain.

Calculation:

According to the graph wind consumption model does not fit exact data.

So we cannot predict the wind energy in the future.

And geothermal consumption model fit exact data.

So we can predict the geothermal consumption using the model.

Hence, we can predict the geothermal consumption using the model.

we cannot predict the wind energy in the future.

e.

To determine

To analysis data on renewable energy.

Answer to Problem 64E

Calculation:

Advantages:

The use renewable energy is sustainable and will never run out.

Disadvantages:

It is difficult to generate the quantity of electricity as large as produced by traditional fossil fuel generators.

Explanation of Solution

Given information:

The table shows the consumption $C$ (in trillions of Btus) of geothermal energy and wind energy in the United States from $2001$ through $2009$ .

  

  

Use your school’s library, the Internet, or some other reference source to research the advantages and disadvantages of using renewable energy.

Calculation:

Advantages:

The use renewable energy is sustainable and will never run out.

Disadvantages:

It is difficult to generate the quantity of electricity as large as produced by traditional fossil fuel generators.