Do the data in the table provide support for the

authors claim that infection with varroa mites

increases a honeybee's susceptibility to secondary

infections?

\begin{equation}

\begin{array}{l}{\text { A) Yes, because the data provide evidence that }} \\ {\text { infection with a pathogen caused the colonies to }} \\ {\text { undergo colony collapse disorder. }} \\ {\text { B) Yes, because for each pathogen, the percent of }} \\ {\text { colonies infected is greater for colonies with }} \\ {\text { colony collapse disorder than for colonies }} \\ {\text { without colony collapse disorder. }}\\{\text { C) No, because the data do not provide evidence }} \\ {\text { about bacteria as a cause of colony collapse }} \\ {\text { disorder. }} \\ {\text { D) No, because the data do not indicate whether the }} \\ {\text { honeybees had been infected with mites. }}\end{array}

\end{equation}

## Discussion

## Video Transcript

No transcript available

## Recommended Questions

Here are box plots of weekly gas prices for regular gas in the United States as reported by the U.S. Energy Information Administration for 2009, 2010, and 2011.

(FIGURE CAN'T COPY)

a) Compare the distribution of prices over the three years.

b) In which year were the prices least stable? Explain.

The figure above shows the average annual gas prices

in the United States from 2003 to $2013 .$ Based on the

information shown, which of the following

conclusions is valid?

$$

\begin{array}{l}{\text { (A) A gallon of gas cost more in } 2008 \text { than in } 2013 .} \\ {\text { (B) The price more than doubled between } 2003 \text { and }} \\ {2013 .}\\{\text { (C) The drop in price from } 2008 \text { to } 2009 \text { was more }} \\ {\text { than } \ $1.00 \text { per gallon. }} \\ {\text { (D) The overall change in price was greater between }} \\ {2003 \text { and } 2008 \text { than it was between } 2008 \text { and }} \\ {2013 .}\end{array}$$

Gasoline Prices In $2013,$ the price of gasoline in the United States inexplicably spiked early and then gradually dropped. The average monthly price (in cents) per gallon of unleaded.regular gasoline for 2013 is shown in the following chart. Find the average rate of change per month in the average price per gallon for each time period. Source: U.S. Energy Information Administration.

(a) From January to March (the peak)

(b) From March to December

(c) From January to December

Which one of the following fuels was used extensively during the Industrial Revolution, leading to increases in levels of carbon dioxide?

a. coal

b. petroleum

c. natural gas

d. solar energy

Concern wind power, which has been used for centuries to propel ships and mill grain. Modern wind power is obtained from windmills that convert wind energy into electricity. Figure 1.65 shows the annual percent growth in US wind power consumption $^{64}$ between 2005 and $2009 .$

(FIGURE CANNOT COPY)

(a) According to Figure $1.65,$ during what single year(s), if any, did the US consumption of wind power energy increase by at least $40 \%$ ? Decrease by at least $40 \% ?$

(b) Did the US consumption of wind power energy double from 2006 to $2008 ?$

The table shows average US retail residential prices of electricity from 2000 to 2012, measured in cents per kilowatt hour.

(a) Make a scatter plot. Is a linear model appropriate?

(b) Find and graph the regression line.

(c) Use your linear model from part (b) to estimate the average retail price of electricity in 2005 and 2013.

Match the description to the type of fuel in the key. Each answer can be used more than once. Each question may have more than one answer.

a. nuclear power

b. fossil fuels

c. hydropower

d. solar power

e. wind power

f. geothermal power.

More available in certain geographic locations

Solar Power. Photovoltaic solar power has become more affordable in recent years. Solar-power plants project that the average cost per watt of electricity generated by solar panels will decrease exponentially as shown in the graph below.

(Graph can't copy)

Assuming that the cost per watt of electricity generated by solar panels will decrease according to the exponential decay model:

a) Using the data for 2009 and $2013,$ find the value of $k,$ and write an exponential function that describes the cost per watt of electricity after time $t,$ in years, where $t$ is the number of years since 2009

b) Estimate the cost per watt of electricity in 2015 and in 2018

c) At this decay rate, in which year will the average cost per watt be $\$ 1.85 ?$

The average annual energy cost for a certain home is

$\$ 4,334 .$ The homeowner plans to spend $\$ 25,000$ to

install a geothermal heating system. The homeowner

estimates that the average annual energy cost will

then be $\$ 2,712 .$ Which of the following inequalities

can be solved to find $t,$ the number of years after

installation at which the total amount of energy cost

savings will exceed the installation cost?

$$

\begin{array}{l}{\text { A) } 25,000>(4,334-2,712) t} \\ {\text { B) } 25,000<(4,334-2,712) t} \\ {\text { C) } 25,000-4,334>2,712 t} \\ {\text { D) } 25,000>\frac{4,332}{2,712} t}\end{array}

$$

Match the description to the type of fuel in the key. Each answer can be used more than once. Each question may have more than one answer.

a. nuclear power

b. fossil fuels

c. hydropower

d. solar power

e. wind power

f. geothermal power.

Renewable source of power

The amount of coal used to generate electricity in the United States is shown in the accompanying table (Energy Information Administration, www.eia.doe.gov).$$\begin{array}{|c|c|c|}\hline\\multicolumn{2}{|c|}\text { Amount } \\\text { Year } & \text { (thousand tons) } & \\

\hline 2001 & 964,433 & \\2002 & 977,507 & \\2003 & 1,005,116 & \\2004 & 1,016,268 & \\2005 & 1,037,485 & \\2006 & 1,026,636 & \text { IMAGE CAN'T COPY } \\2007 & 1,046,424 & \\\hline\end{array}$$

a. Use linear regression on your graphing calculator to find the regression equation. Let $x=1$ correspond to 2001

b. Use the regression equation to predict the amount of coal used for clectricity in 2010 .

c. Interpret the slope of the regression equation.

If future projections are that the number of farms in the United

States will decrease by 5$\%$ from 2010 to 2030 and that the average

size of farms will decrease from 2010 to 2030 by the same percent

as the decrease from 1990 to $2010,$ which of the following is

closest to the total number of acres of farmland, in millions of

acres, in the United States in 2030$?$

$$\begin{array}{l}{\text { (A) } 750} \\ {\text { (B) } 800} \\ {\text { (C) } 850} \\ {\text { (D) } 900}\end{array}$$

Match the description to the type of fuel in the key. Each answer can be used more than once. Each question may have more than one answer.

a. nuclear power

b. fossil fuels

c. hydropower

d. solar power

e. wind power

f. geothermal power.

Contribute(s) to global warming

The following table gives the total world emissions of $\mathrm{CO}_{2}$ from fossil fuels, in billions of tons per year. $^{3}$

(a) Usc this data to cstimate the total world $\mathrm{CO}_{2}$ cmissions between 1981 and 2011 using a left sum with $n=6$

(b) Is your answer in part (a) an upper or lower estimate? How can you tell?

(c) Use this data to estimate the total world $\mathrm{CO}_{2}$ emissions between 1981 and 2011 using a right sum with $n=3$

(d) Is your answer in part (c) an upper or lower estimate? How can you tell?

The scatterplot below shows the amount of electric

energy generated, in millions of megawatt-hours, by

nuclear sources over a 10 -year period.

Of the following equations, which best models the

data in the scatterplot?

$$

\begin{array}{l}{\text { A) } y=1.674 x^{2}+19.76 x-745.73} \\ {\text { B) } y=-1.674 x^{2}-19.76 x-745.73} \\ {\text { C) } y=1.674 x^{2}+19.76 x+745.73} \\ {\text { D) } y=-1.674 x^{2}+19.76 x+745.73}\end{array}

$$

Match the description to the type of fuel in the key. Each answer can be used more than once. Each question may have more than one answer.

a. nuclear power

b. fossil fuels

c. hydropower

d. solar power

e. wind power

f. geothermal power.

Detrimental environmental effects

The average residential electrical power use (in hundreds of watts) per hour is given in the following table.

a. Compute the average total energy used in a day in kilowatt-hours (kWh).

b. If a ton of coal generages 1842 $\mathrm{kWh}$ , how long does it take for an average residence to burn a ton of coal?

c. Explain why the data might fit a plot of the form $p(t)=11.5-7.5 \sin \left(\frac{\pi t}{12}\right)$

A typical nuclear power plant generates electricity at the rate of 1000 MW. The efficiency of transforming thermal energy into electrical energy is $\frac{1}{3}$ and the plant runs at full capacity for $80 \%$ of the year. (Nuclear power plants are down about $20 \%$ of the time for maintenance and refueling.)

A. How much thermal energy does the plant generate in one year?

b. What mass of uranium is transformed into energy in one year?

Repeat Prob. $2-82$ assuming the electricity is produced by a power plant that burns coal. The average production of $\mathrm{CO}_{2}$ in this case is $1.1 \mathrm{kg}$ per $\mathrm{kWh}$.

Match the description to the type of fuel in the key. Each answer can be used more than once. Each question may have more than one answer.

a. nuclear power

b. fossil fuels

c. hydropower

d. solar power

e. wind power

f. geothermal power.

Waste products are harmful

Why do water turbines seem more promising than tidal basins for producing electric energy?

(a) Turbines are less expensive to build.

(b) Turbines have less impact on the environment.

(c) There are many more locations for turbines than for tidal basins.

(d) Turbines can operate 24 hours/day versus for only 10 hours/day for tidal basins.

(e) All of the above

The table shows U.S. energy production for a number of years.

a. Find a linear model, a cubic model, and a quartic model for the data set. Let 0 represent $1960 .$

b. Graph each model. Compare the three models to determine which fits best.

c. Use your answer to part (b) to estimate U.S. energy production in 1997 .

What source of energy is the United States most dependent on today? How does this compare to 100 years ago?

The average residential electrical power use (in hundreds of watts) per hour is given in the following table.

a. Compute the average total energy used in a day in kilowatt-hours (kWh).

b. If a ton of coal generates 1842 kWh, how long does it take for an average residence to burn a ton of coal?

c. Explain why the data might fit a plot of the form $p(t)=11.5-7.5 \sin \left(\frac{\pi t}{12}\right).$

World annual natural gas $^{8}$ consumption, $N,$ in millions of metric tons of oil equivalent, is approximated by $N=$ $1770+53 t,$ where $t$ is in years since 1990

(a) How much natural gas was consumed in $1990 ?$ In $2010 ?$

(b) Estimate the total amount of natural gas consumed during the 20 -year period from 1990 to 2010 .

Use the following graph, which shows the portion of home energy spending that goes toward each category.

Suppose a family spent $\$ 1860$ per year on energy for their home.

a. How much was spent heating and cooling their home?

b. How much was spent for lighting and appliances?

c. How much was spent heating water?

d. How much was spent on refrigeration?

(THE GRAPH CANNOT COPY)

The bar graph above shows renewable energy

consumption in quadrillions of British thermal units

(Btu) in the United States, by energy source, for several

energy sources in the years 2000 and $2010 .$

In a scatterplot of this data, where renewable energy

consumption in the year 2000 is plotted along the

$x$ -axis and renewable energy consumption in the year

2010 is plotted along the $y$ -axis for each of the given

energy sources, how many data points would be

above the line $y=x$ ?

A) 1

B) 2

C) 3

D) 4

For a new type of biofuel, scientists estimate that it takes $A=f(g)$ gallons of gasoline to produce the raw materials to generate $g$ gallons of biofuel. Assume the biofuel is equal in efficiency to the gasoline.

(a) At a certain level of production, we have $d A / d g=$

1.3. Interpret this in practical terms. Is this level of production sustainable? Explain.

(b) Repeat part (a) if $d A / d g=0.2$

For a new type of biofuel, scientists estimate that it takes $A=f(g)$ gallons of gasoline to produce the raw materials to generate $g$ gallons of biofuel. Assume the biofuel is equal in efficiency to the gasoline.

(a) At a certain level of production, we have $d A / d g=$

1.3. Interpret this in practical terms. Is this level of production sustainable? Explain.

(b) Repeat part (a) if $d A / d g=0.2$

Energy cost for a Car The cost of the electricity needed to

drive an all-electric car is about 4 cents per mile. The cost of

the gasoline needed to drive the average gasoline-powered

car is about 12 cents per mile.

(a) Find a formula that models the energy cost $C$ of driving

$x$ miles for (i) the all-electric car and (ii) the average

gasoline-powered car.

(b) Find the cost of driving $10,000$ mi with each type of car.

The price of energy does not reflect its real costs. What kinds of hidden environmental costs are not reflected in the price of fossil fuels? How are these costs paid, and by whom? Do you think these costs could or should be figured into the price of oil? How might that be done?

The circle graph shows how a typical household spends money on energy. Find each of the following.

FIGURE CAN'T COPY.

$$\mathrm{m} \widehat{R Q}$$

What is the ultimate source of energy for fossil fuels, dams, and windmills?

Solve.

Wind Power. U.S. wind-power capacity has grown exponentially from about 2000 megawatts in 1990 to $35,000$ megawatts in 2009.

a) Find the exponential growth rate $k,$ and write an equation for an exponential function that can be used to predict U.S. wind-power capacity $t$ years after 1990

b) Estimate the year in which wind-power capacity will reach $50,000$ megawatts.

(II) If a typical house requires 960 W of electric power on average, what minimum amount of deuterium fuel would have to be used in a year to supply these electrical needs? Assume the reaction of Eq. 31$-$8b.

Gasoline Prices In 2008, the price of gasoline in the United States inexplicably spiked and then dropped. The average monthly price (in cents) per gallon of unleaded regular gasoline for 2008 is shown in the following chart. Find the average rate of change per month in the average price per gallon for each time period.

a. From January to July (the peak)

b. From July to December

c. From January to December

It is estimated that the total explosive yield of all the nuclear bombs in existence currently is about $4,000 \mathrm{MT}$ .

(a) Convert this amount of energy to kilowatt-hours, noting that $1 \mathrm{kW} \cdot \mathrm{h}=3.60 \times 10^{6} \mathrm{J}$ .

(b) What would the monetary value of this energy be if it could be converted to electricity costing 10 cents per kw-h?

Use the following graph, which shows the average price for regular gasoline at the beginning of January of each year.

CAN'T COPY THE GRAPH

What was the percent of increase in the average price of a gallon of gasoline from January 2009 to January $2010 ?$

Renewable resources

a. are in limited supply compared to nonrenewable resources.

b. are always forthcoming but still may be inadequate for human needs.

c. include such energy sources as wind, solar, and biomass.

d. All of these are correct.

Which type or types of nuclear reactors have these characteristics?

$\begin{array}{l}{\text { (a) Can use natural uranium as a fuel }} \\ {\text { (b) Does not use a moderator }} \\ {\text { (c) Can be refueled without shutting down }}\end{array}$

The world’s uranium supply is approximately $10^{9} \mathrm{kg}\left(10^{6} \text { tons), } 0.7 \% \text { of which is }^{235} \mathrm{U}\right.$ (a) How much energy is available from the fission of this $^{235}\mathrm{U}$? (b) The world’s energy consumption rate for production of electricity is about $10^{20} \mathrm{J} /$ year. At this rate, how many years would the uranium last if it were used to provide all our electrical energy?

Biodiesel Production The table shows the biodiesel productions $y$ (in thousands of barrels per day) for the United States for 2007 through $2012 .$ The variable $t$ represents the time in years, with $t=7$ corresponding to $2007 .$ (Source: U.S. Energy Information Administration)

$$\begin{array}{|c|c|c|c|c|c|c|}\hline t & {7} & {8} & {9} & {10} & {11} & {12} \\ \hline y & {32} & {44} & {34} & {22} & {63} & {64} \\ \hline\end{array}$$

(a) Plot the data by hand and connect adjacent points with a line segment. Use the slope of each line segment to determine the year when biodiesel production increased most rapidly.

(b) Find the average rate of change of biodiesel production for the United States from 2007 through 2012.

(c) Should the average rate of change be used to predict future biodiesel production? Explain.

Use the following graph, which shows the average price for regular gasoline at the beginning of January of each year.

CAN'T COPY THE GRAPH

What was the percent of decrease in the average price of a gallon of gasoline from January 2008 to January $2009 ?$

The Energy Information Administration reported that the mean retail price per gallon of

regular grade gasoline was $\$ 2.81$ (Energy Information Administration, November $2010 ) .$

Suppose that the standard deviation was $S .10$ and that the retail price per gallon has a bell-

shaped distribution.

a. What percentage of regular grade gasoline sold between $\$ 2.71$ and $\$ 2.91$ per gallon?

b. What percentage of regular grade gasoline sold between $\$ 2.71$ and $\$ 3.01$ per gallon?

c. What percentage of regular grade gasoline sold for more than $\$ 3.01$ per gallon?

Battery-powered electricity is very expensive compared with that available from a wall receptacle. Estimate the cost per kWh of ($a$) an alkaline D-cell (cost $\$$1.70) and ($b$) an alkaline AA-cell (cost $\$$1.25). These batteries can provide a continuous current of 25 mA for 820 h and 120 h, respectively, at 1.5 V. ($c$) Compare to the cost of a normal 120-V ac house source at $\$$0.10/kWh.

Use the following graph, which shows the portion of home energy spending that goes toward each category.

Suppose a family spent $\$ 1640$ per year on energy for their home.

a. How much was spent heating and cooling their home?

b. How much was spent for lighting and appliances?

c. How much was spent heating water?

d. How much was spent on refrigeration?

(THE GRAPH CANNOT COPY)

Use the data for the United States in this table to answer the following questions.

$$\begin{array}{ll}{\text { Year }} & {\text { Real GDP per Capita }(2009 \text { prices) }} \\ {2010} & {\$ 47,719} \\ {2011} & {48,116} \\ {2012} & {48,822} \\ {2013} & {49,184} \\ {2014} & {50,010}\end{array}$$

a. What was the percentage change in real GDP per capita between 2010 and 2014$?$

b. What was the average annual growth rate in real GDP per capita between 2010 and 2014$?$ (Hint: Remember that the average annual growth rate for relatively short periods can be approximated by averaging the growth rates for each year during the period [see Chapter 10$]$ .)

(II) Suppose a fusion reactor ran on "d$-$d" reactions, Eqs. 31$-$8a and b in equal amounts. Estimate how much natural water, for fuel, would be needed per hour to run a 1150-MW reactor, assuming 33$\%$ efficiency.

Battery-powered electricity is very expensive compared with that available from a wall receptacle. Estimate the cost per kWh of $(a)$ an alkaline D-cell (cost $\$ 1.70 )$ and $(b)$ an alkaline AA-cell (cost $\$ 1.25$ ). These batteries can provide a continuous current of 25 $\mathrm{mA}$ for 820 $\mathrm{h}$ and 120 $\mathrm{h}$ , respectively, at 1.5 $\mathrm{V}$ . Compare to normal 120 $\mathrm{-V}$ ac house current at $\$ 0.10 / \mathrm{kWh}$ .

For a certain coal-burning power plant, the cost to remove pollutants from plant emissions can be modeled by $C(p)=\frac{80 p}{100-p},$ where $C(p)$ represents the cost (in thousands of dollars) to remove $p$ percent of the pollutants. (a) Find the cost to remove $20 \%, 50 \%,$ and $80 \%$ of the pollutants, then comment on the results; (b) graph the function using an appropriate scale; and (c) use the direction/approach notation to state what happens if the power company attempts to remove $100 \%$ of the pollutants.

In a recent year, wind machines in the United States generated 17.8 billion kilowatt-hours of electricity, enough to serve over 1.6 million households. The nation's total electricity production that year was 4450 billion kilowatt-hours. (Source: Energy Information Administration) What percent of the total energy production was generated by wind machines?

A transition to hydrogen fuel technology will

a. be long in coming and not likely to be of major significance.

b. lessen many current environmental problems.

c. not be likely because it will always be expensive and as polluting as natural gas.

d. be of major consequence, but resource limitations for obtaining hydrogen will hinder its progress.

The Office of Coal, Nuclear, Electric and Alternate Fuels reported the following data as the costs (in cents) of the average revenue per kilowatt-hour for sectors in Arkansas:

$$\begin{array}{lllllllll}

\hline 6.61 & 7.61 & 6.99 & 7.48 & 5.10 & 7.56 & 6.65 & 5.93 & 7.92 \\

5.52 & 7.47 & 6.79 & 8.27 & 7.50 & 7.44 & 6.36 & 5.20 & 5.48 \\

7.69 & 8.74 & 5.75 & 6.94 & 7.70 & 6.67 & 4.59 & 5.96 & 7.26 \\

5.38 & 8.88 & 7.49 & 6.89 & 7.25 & 6.89 & 6.41 & 5.86 & 8.04 \\

\hline

\end{array}$$

a. Prepare a grouped frequency distribution for the average revenue per kilowatt-hour using class boundaries 4,5,6,7,8,9

b. Find the class width.

c. List the class midpoints.

d. Construct a relative frequency histogram of these data.

Do you expect the average rate of change (in units per year) of each of the following to be positive or negative? Explain your reasoning.

(a) Number of acres of rain forest in the world.

(b) Population of the world.

(c) Number of polio cases each year in the US, since 1950

(d) Height of a sand dune that is being eroded.

(e) Cost of living in the US.

The circle graph shows how a typical household spends money on energy. Find each of the following.

FIGURE CAN'T COPY.

$$\mathrm{m} \widehat{U T}$$

Use the following graph, which shows the average price for regular gasoline at the beginning of January of each year.

CAN'T COPY THE GRAPH

What was the percent of increase in the average price of a gallon of gasoline from January 2000 to January $2010 ?$

Which of the following best approximates the

average rate of change in the annual budget for

agriculture/natural resources in Kansas from 2008 to

2010$?$

$$\begin{array}{ll}{\text { A) }} { 50,000,000 \text { per year }} \\ {\text { B) }} { 65,000,000 \text { per year }} \\ {\text { C) }} { 75,000,000 \text { per year }} \\ {\text { D) } 130,000,000 \text { per year }}\end{array}$$

What is the ultimate source of energy in coal, oil, and wood? Why do we call energy from wood renewable but energy from coal and oil nonrenewable?

The circle graph shows how a typical household spends money on energy. Find each of the following.

FIGURE CAN'T COPY.

$$\mathrm{m} \widehat{U P T}$$

The following bar graph shows the capacity of the United States to generate electricity from the wind in the years shown.

(GRAPH CANNOT COPY)

Find the approximate increase in megawatt capacity during the 2 -year period from 2004 to 2006

Cost of Natural Gas In April 2014, Nicor Gas had the following rate schedule for natural gas usage in small businesses.

$$

\begin{array}{cl}{\text { Monthly customer charge }} & {\$ 72.60} \\ {\text { Distribution charge }} \\ {1 \text { st } 150 \text { therms }} & {\$ 0.1201 / \text { therm }} \\ {\text { Next } 4850 \text { therms }} & {\$ 0.0549 / \text { therm }} \\ {\text { Over } 5000 \text { therms }} & {\$ 0.0482 / \text { therm }} \\ {\text { Gas supply charge }} & {\$ 0.68 / \text { therm }}\end{array}

$$

(a) What is the charge for using 1000 therms in a month?

(b) What is the charge for using 6000 therms in a month?

(c) Develop a function that models the monthly charge $C$ for $x$ therms of gas.

(d) Graph the function found in part ( $\mathrm{c})$.

The average energy output of a good grade of coal is $2.6 \times 10^{7} \mathrm{kJ} /$ ton. Fission of $1 \mathrm{mol}$ of $^{235} \mathrm{U}$ releases $2.1 \times 10^{10} \mathrm{kJ} .$ Find the number of tons of coal needed to produce the same energy as 1 lb of $^{235} \mathrm{U}$. (See Appendix C for conversion factors.)

Wind Energy In Exercise 25 of Section $7.3,$ we estimated

the total wind energy consumption (in trillion BTUs) for the

12 -year period from 2001 to 2013 using rectangles and the fol-

lowing data. Source: Annual Energy Review.

$$\begin{array}{ll}{\text { Year }} & {\text { Consumption }} \\ {2001} & {70} \\ {2004} & {142} \\ {2007} & {341} \\ {2010} & {923} \\ {2013} & {1595}\end{array}$$

$$\begin{array}{l}{\text { (a) Approximate the total wind energy consumption using the }} \\ {\text { trapezoidal rule. }} \\ {\text { (b) Approximate the total wind energy consumption using }} \\ {\text { Simpson's rule. }}\end{array}$$

There is a trend in the United States toward using coal-fired power plants to generate electricity rather than building new nuclear fission power plants. Is the use of coal-fired power plants without risk? Make a list of the risks to society from the use of each type of power plant.

There is a trend in the United States toward using coal-fired power plants to generate electricity rather than building new nuclear fission power plants. Is the use of coal-fired power plants without risk? Make a list of the risks to society from the use of each type of power plant.

Use the following graph, which shows the average price for regular gasoline at the beginning of January of each year.

CAN'T COPY THE GRAPH

What was the percent of increase in the average price of a gallon of gasoline from January 2007 to January $2008 ?$

FUEL CONSUMPTION The daily consumption $C$ (in gallons) of diesel fuel on a farm is modeled by

$C =\ 30.3 + 21.6\ sin(\dfrac{2 \pi t}{365} + 10.9)$

where $t$ is the time (in days), with $t=1$ corresponding to January 1.

(a) What is the period of the model? Is it what you expected? Explain.

(b) What is the average daily fuel consumption? Which term of the model did you use? Explain.

(c) Use a graphing utility to graph the model. Use the graph to approximate the time of the year when consumption exceeds 40 gallons per day.

The data in the following table are used to estimate the average power output produced by Peter Sagan for each of the last 18 sec of Stage 1 of the 2012 Tour de France.

Estimate the net energy used in kilojoules (kJ), noting that 1W = 1 J/s, and the average power output by Sagan during this time interval.

Global Carbon Emissions from Fossil Fuel Burning

(TABLE CAN'T COPY)

Climate Change: Global Warming. What is the average rate of change in global carbon emissions from fossil fuel burning from

a. 1900 to $1950 ?$

b. 1950 to $2000 ?$

In Exercises 53 and $54,$ use the following information. From 1989 through $1993,$ the amounts (in billions of dollars) spent on natural gas $N$ and electricity $E$ by United States residents can be modeled by the following equations, where $t$ is the number of years since $1989 .$

$$\text {Gas spending model:} N=1.488 t^{2}-3.403 t+65.590$$

$$\text {Electricity spending model:} E=-0.107 t^{2}+6.897 t+169.735$$

According to the models, will more money be spent on natural gas or on electricity in $2020 .$ HINT: It may be helpful to graph the equations on a graphing calculator to answer this question.

Solve each problem.

Electricity charges. Texas Power installed a power line from a transformer at $(-311,322)$ to the well at $(185,234)$ as shown in the figure for $\$ 116$ per yard.

a) What was the cost to the nearest dollar for the power line?

b) What is the location of the pole used at the midpoint?

(GRAPH NOT COPY)

In one year the United States consumption of electrical energy was about $2.2 \times 10^{12} \mathrm{kW} \cdot$ h. (a) How much mass is equivalent to the consumed energy in that year? (b) Does it make any difference to your answer if this energy is generated in oil-burning, nuclear, or hydroelectric plants?

Cost of Natural Gas In March 2014 , Laclede Gas had the rate schedule (on, right) for natural gas usage in single-family residences.

(a) What is the charge for using 20 therms in a month?

(b) What is the charge for using 150 therms in a month?

(c) Develop a function that models the monthly charge $C$ for $x$ therms of gas.

(d) Graph the function found in part $(\mathrm{c})$.

$$

\begin{array}{cl}{\text { Monthly service charge }} & {\$ 19.50} \\ {\text { Delivery charge }} \\ {\text { First } 30 \text { therms }} & {\$ 0.91686 / \text { therm }} \\ {\text { Over } 30 \text { therms }} & {\$ 0} \\ {\text { Natural gas cost }} \\ {\text { First } 30 \text { therms }} & {\$ 0.3313 / \text { therm }}\\ {\text { Over } 30 \text { therms }} & {\$ 0.5757 / \text { therm }}\end{array}

$$

The following bar graph shows the capacity of the United States to generate electricity from the wind in the years shown.

(GRAPH CANNOT COPY)

Find the approximate increase in megawatt capacity during the 2 -year period from 2001 to 2003 .

Heating Fuels Which type of graph would you use to depict how many households heat with gas, oil, or electricity? Explain.