Use geometric formulas to find the area between the graphs of $y=f(x)$ and $y=g(x)$ over the indicated interval. (If necessary, review Appendix $\mathrm{C}$ ).

$$

f(x)=60, g(x)=45 ;[2,12]

$$

Narayan H.

Numerade Educator

Use geometric formulas to find the area between the graphs of $y=f(x)$ and $y=g(x)$ over the indicated interval. (If necessary, review Appendix $\mathrm{C}$ ).

$$

f(x)=-30, g(x)=20 ;[-3,6]

$$

Narayan H.

Numerade Educator

Use geometric formulas to find the area between the graphs of $y=f(x)$ and $y=g(x)$ over the indicated interval. (If necessary, review Appendix $\mathrm{C}$ ).

$$

f(x)=6+2 x, g(x)=6-x ;[0,5]

$$

Narayan H.

Numerade Educator

Use geometric formulas to find the area between the graphs of $y=f(x)$ and $y=g(x)$ over the indicated interval. (If necessary, review Appendix $\mathrm{C}$ ).

$$

f(x)=0.5 x, g(x)=0.5 x-4 ;[0,8]

$$

Narayan H.

Numerade Educator

Use geometric formulas to find the area between the graphs of $y=f(x)$ and $y=g(x)$ over the indicated interval. (If necessary, review Appendix $\mathrm{C}$ ).

$$

f(x)=-3-x, g(x)=4+2 x ;[-1,2]

$$

Narayan H.

Numerade Educator

Use geometric formulas to find the area between the graphs of $y=f(x)$ and $y=g(x)$ over the indicated interval. (If necessary, review Appendix $\mathrm{C}$ ).

$$

f(x)=100-2 x, g(x)=10+3 x ;[5,10]

$$

Narayan H.

Numerade Educator

Use geometric formulas to find the area between the graphs of $y=f(x)$ and $y=g(x)$ over the indicated interval. (If necessary, review Appendix $\mathrm{C}$ ).

$$

f(x)=x, g(x)=\sqrt{4-x^{2}} ;[0, \sqrt{2}]

$$

Narayan H.

Numerade Educator

Use geometric formulas to find the area between the graphs of $y=f(x)$ and $y=g(x)$ over the indicated interval. (If necessary, review Appendix $\mathrm{C}$ ).

$$

f(x)=\sqrt{16-x^{2}}, g(x)=|x| ;[-2 \sqrt{2}, 2 \sqrt{2}]

$$

Bobby B.

University of North Texas

Refer to Figures A-D. Set up definite integrals in Problems 9-12 that represent the indicated shaded area.

Shaded area in Figure $\mathrm{B}$

Bobby B.

University of North Texas

Refer to Figures A-D. Set up definite integrals in Problems 9-12 that represent the indicated shaded area.

Shaded area in Figure A

Bobby B.

University of North Texas

Refer to Figures A-D. Set up definite integrals in Problems 9-12 that represent the indicated shaded area.

Shaded area in Figure $\mathrm{C}$

Bobby B.

University of North Texas

Refer to Figures A-D. Set up definite integrals in Problems 9-12 that represent the indicated shaded area.

Shaded area in Figure $\mathrm{D}$

Bobby B.

University of North Texas

Refer to Figures A-D. Set up definite integrals in Problems 9-12 that represent the indicated shaded area.

Explain why $\int_{a}^{b} h(x) d x$ does not represent the area between the graph of $y=h(x)$ and the $x$ axis from $x=a$ to $x=b$ in Figure $\mathrm{C}$.

Bobby B.

University of North Texas

Refer to Figures A-D. Set up definite integrals in Problems 9-12 that represent the indicated shaded area.

Explain why $\int_{a}^{b}[-h(x)] d x$ represents the area between the graph of $y=h(x)$ and the $x$ axis from $x=a$ to $x=b$ in Figure $\mathrm{C}$.

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=x+4 ; y=0 ; 0 \leq x \leq 4

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=-x+10 ; y=0 ;-2 \leq x \leq 2

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=x^{2}-20 ; y=0 ;-3 \leq x \leq 0

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=x^{2}+2 ; y=0 ; 0 \leq x \leq 3

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=-x^{2}+10 ; y=0 ;-3 \leq x \leq 3

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=-2 x^{2} ; y=0 ;-6 \leq x \leq 0

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=x^{3}+1 ; y=0 ; 0 \leq x \leq 2

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=-x^{3}+3 ; y=0 ;-2 \leq x \leq 1

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=x(1-x) ; y=0 ;-1 \leq x \leq 0

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=-x(3-x) ; y=0 ; 1 \leq x \leq 2

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=-e^{x} ; y=0 ;-1 \leq x \leq 1

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=e^{x} ; y=0 ; 0 \leq x \leq 1

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=\frac{1}{x} ; y=0 ; 1 \leq x \leq e

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

$$

y=-\frac{1}{x} ; y=0 ;-1 \leq x \leq-\frac{1}{e}

$$

Narayan H.

Numerade Educator

Base your answers on the Gini index of income concentration (see Table 2, page 388).

In which of Canada, Mexico, or the United States is income most equally distributed? Most unequally distributed?

Bobby B.

University of North Texas

Base your answers on the Gini index of income concentration (see Table 2, page 388).

In which of France, Germany, or Sweden is income most equally distributed? Most unequally distributed?

Bobby B.

University of North Texas

Base your answers on the Gini index of income concentration (see Table 2, page 388).

In which of Brazil, India, or Jordan is income most equally distributed? Most unequally distributed?

Bobby B.

University of North Texas

Base your answers on the Gini index of income concentration (see Table 2, page 388).

In which of China, Japan, or Russia is income most equally distributed? Most unequally distributed?

Bobby B.

University of North Texas

Refer to Figures $A$ and $B$. Set up definite integrals in Problems $33-40$ that represent the indicated shaded areas over the given intervals.

Over interval $[a, b]$ in Figure $A$

Bobby B.

University of North Texas

Refer to Figures $A$ and $B$. Set up definite integrals in Problems $33-40$ that represent the indicated shaded areas over the given intervals.

Over interval $[c, d]$ in Figure $A$

Bobby B.

University of North Texas

Refer to Figures $A$ and $B$. Set up definite integrals in Problems $33-40$ that represent the indicated shaded areas over the given intervals.

Over interval $[b, d]$ in Figure $A$

Bobby B.

University of North Texas

Refer to Figures $A$ and $B$. Set up definite integrals in Problems $33-40$ that represent the indicated shaded areas over the given intervals.

Over interval $[a, c]$ in Figure A

Bobby B.

University of North Texas

Refer to Figures $A$ and $B$. Set up definite integrals in Problems $33-40$ that represent the indicated shaded areas over the given intervals.

Over interval $[c, d]$ in Figure $\mathrm{B}$

Bobby B.

University of North Texas

Refer to Figures $A$ and $B$. Set up definite integrals in Problems $33-40$ that represent the indicated shaded areas over the given intervals.

Over interval $[a, b]$ in Figure $B$

Bobby B.

University of North Texas

Refer to Figures $A$ and $B$. Set up definite integrals in Problems $33-40$ that represent the indicated shaded areas over the given intervals.

Over interval $[a, c]$ in Figure $B$

Bobby B.

University of North Texas

Refer to Figures $A$ and $B$. Set up definite integrals in Problems $33-40$ that represent the indicated shaded areas over the given intervals.

Over interval $[b, d]$ in Figure $B$

Bobby B.

University of North Texas

Refer to Figures $A$ and $B$. Set up definite integrals in Problems $33-40$ that represent the indicated shaded areas over the given intervals.

Referring to Figure $\mathrm{B}$, explain how you would use definite integrals and the functions $f$ and $g$ to find the area bounded by the two functions from $x=a$ to $x=d$.

Bobby B.

University of North Texas

Refer to Figures $A$ and $B$. Set up definite integrals in Problems $33-40$ that represent the indicated shaded areas over the given intervals.

Referring to Figure A, explain how you would use definite integrals to find the area between the graph of $y=f(x)$ and the $x$ axis from $x=a$ to $x=d$.

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=-x ; y=0 ;-2 \leq x \leq 1

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=-x+1 ; y=0 ;-1 \leq x \leq 2

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=x^{2}-4 ; y=0 ; 0 \leq x \leq 3

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=4-x^{2} ; y=0 ; 0 \leq x \leq 4

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=x^{2}-3 x ; y=0 ;-2 \leq x \leq 2

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=-x^{2}-2 x ; y=0 ;-2 \leq x \leq 1

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=-2 x+8 ; y=12 ;-1 \leq x \leq 2

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=2 x+6 ; y=3 ;-1 \leq x \leq 2

$$

Narayan H.

Numerade Educator

$$

y=2 x+6 ; y=3 ;-1 \leq x \leq 2

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=x^{2} ; y=9

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=4-x^{2} ; y=-5

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=x^{2}-1 ; y=3

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=x^{2}+1 ; y=2 x-2 ;-1 \leq x \leq 2

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=x^{2}-1 ; y=x-2 ;-2 \leq x \leq 1

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=e^{0.5 x} ; y=-\frac{1}{x} ; 1 \leq x \leq 2

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.

$$

y=\frac{1}{x} ; y=-e^{x} ; 0.5 \leq x \leq 1

$$

Bobby B.

University of North Texas

Set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. [Hint: A circle of radius $r$, with center at the origin, has equation $x^{2}+y^{2}=r^{2}$ and area $\left.\pi r^{2}\right] .$

$$

y=\sqrt{9-x^{2} ;} y=0 ;-3 \leq x \leq 3

$$

Narayan H.

Numerade Educator

Set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. [Hint: A circle of radius $r$, with center at the origin, has equation $x^{2}+y^{2}=r^{2}$ and area $\left.\pi r^{2}\right] .$

$$

y=\sqrt{25-x^{2}} ; y=0 ;-5 \leq x \leq 5

$$

Narayan H.

Numerade Educator

Set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. [Hint: A circle of radius $r$, with center at the origin, has equation $x^{2}+y^{2}=r^{2}$ and area $\left.\pi r^{2}\right] .$

$$

y=-\sqrt{16-x^{2}} ; y=0 ; 0 \leq x \leq 4

$$

Narayan H.

Numerade Educator

Set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. [Hint: A circle of radius $r$, with center at the origin, has equation $x^{2}+y^{2}=r^{2}$ and area $\left.\pi r^{2}\right] .$

$$

y=-\sqrt{36-x^{2}} ; y=0 ;-6 \leq x \leq 0

$$

Narayan H.

Numerade Educator

Set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. [Hint: A circle of radius $r$, with center at the origin, has equation $x^{2}+y^{2}=r^{2}$ and area $\left.\pi r^{2}\right] .$

$$

y=-\sqrt{4-x^{2}} ; y=\sqrt{4-x^{2}} ;-2 \leq x \leq 2

$$

Narayan H.

Numerade Educator

Set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. [Hint: A circle of radius $r$, with center at the origin, has equation $x^{2}+y^{2}=r^{2}$ and area $\left.\pi r^{2}\right] .$

$$

y=-\sqrt{100-x^{2}} ; y=\sqrt{100-x^{2}} ;-10 \leq x \leq 10

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.

$$

y=e^{x} ; y=e^{-x} ; 0 \leq x \leq 4

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.

$$

y=e^{x} ; y=-e^{-x} ; 1 \leq x \leq 2

$$

Narayan H.

Numerade Educator

Find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.

$$

y=x^{3} ; y=4 x

$$

Bobby B.

University of North Texas

$$

y=x^{3} ; y=4 x

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.

$$

y=x^{3}+1 ; y=x+1

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.

$$

y=x^{3}-3 x^{2}-9 x+12 ; y=x+12

$$

Bobby B.

University of North Texas

Find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.

$$

y=x^{3}-6 x^{2}+9 x ; y=x

$$

Bobby B.

University of North Texas

Use a graphing calculator to graph the equations and find relevant intersection points. Then find the area bounded by the curves. Compute answers to three decimal places.

$$

y=x^{3}-x^{2}+2 ; y=-x^{3}+8 x-2

$$

Bobby B.

University of North Texas

Use a graphing calculator to graph the equations and find relevant intersection points. Then find the area bounded by the curves. Compute answers to three decimal places.

$$

y=e^{-x} ; y=3-2 x

$$

Bobby B.

University of North Texas

Use a graphing calculator to graph the equations and find relevant intersection points. Then find the area bounded by the curves. Compute answers to three decimal places.

$$

y=2-(x+1)^{2} ; y=e^{x+1}

$$

Bobby B.

University of North Texas

Use a graphing calculator to graph the equations and find relevant intersection points. Then find the area bounded by the curves. Compute answers to three decimal places.

$$

y=e^{x} ; y=5 x-x^{3}

$$

Bobby B.

University of North Texas

Use a graphing calculator to graph the equations and find relevant intersection points. Then find the area bounded by the curves. Compute answers to three decimal places.

$$

y=2-e^{x} ; y=x^{3}+3 x^{2}

$$

Bobby B.

University of North Texas

Use a numerical integration routine on a graphing calculator to find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.

$$

y=e^{-x} ; y=\sqrt{\ln x ;} 2 \leq x \leq 5

$$

Wendi Z.

Numerade Educator

Use a numerical integration routine on a graphing calculator to find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.

$$

y=x^{2}+3 x+1 ; y=e^{e^{x}} ;-3 \leq x \leq 0

$$

Wendi Z.

Numerade Educator

Use a numerical integration routine on a graphing calculator to find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.

$$

y=e^{x^{2}} ; y=x+2

$$

Wendi Z.

Numerade Educator

Use a numerical integration routine on a graphing calculator to find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.

$$

y=\ln (\ln x) ; y=0.01 x

$$

Wendi Z.

Numerade Educator

Find the constant $c$ ( to 2 decimal places) such that the Lorenz curve $f(x)=x^{c}$ has the given Gini index of income concentration.

$$

0.52

$$

Bobby B.

University of North Texas

Find the constant $c$ ( to 2 decimal places) such that the Lorenz curve $f(x)=x^{c}$ has the given Gini index of income concentration.

$$

0.23

$$

Bobby B.

University of North Texas

Find the constant $c$ ( to 2 decimal places) such that the Lorenz curve $f(x)=x^{c}$ has the given Gini index of income concentration.

$$

0.29

$$

Bobby B.

University of North Texas

Find the constant $c$ ( to 2 decimal places) such that the Lorenz curve $f(x)=x^{c}$ has the given Gini index of income concentration.

$$

0.65

$$

Bobby B.

University of North Texas

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

Using production and geological data, the management of an oil company estimates that oil will be pumped from a producing field at a rate given by

$$

R(t)=\frac{100}{t+10}+10 \quad 0 \leq t \leq 15

$$

where $R(t)$ is the rate of production (in thousands of barrels per year) $t$ years after pumping begins. Find the area between the graph of $R$ and the $t$ axis over the interval [5,10] and interpret the results.

Bobby B.

University of North Texas

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

In Problem $85,$ if the rate is found to be

$$

R(t)=\frac{100 t}{t^{2}+25}+4 \quad 0 \leq t \leq 25

$$

then find the area between the graph of $R$ and the $t$ axis over the interval [5,15] and interpret the results.

Bobby B.

University of North Texas

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

An amusement company maintains records for each video game it installs in an arcade. Suppose that $C(t)$ and $R(t)$ represent the total accumulated costs and revenues (in thousands of dollars), respectively, $t$ years after a particular game has been installed. If

$$

C^{\prime}(t)=2 \quad \text { and } \quad R^{\prime}(t)=9 e^{-0.3 t}

$$

then find the area between the graphs of $C^{\prime}$ and $R^{\prime}$ over the interval on the $t$ axis from 0 to the useful life of the game and interpret the results.

Wendi Z.

Numerade Educator

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

Repeat Problem 87 if

$$

C^{\prime}(t)=2 t \quad \text { and } \quad R^{\prime}(t)=5 t e^{-0.1 t^{2}}

$$

Wendi Z.

Numerade Educator

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

In a study on the effects of World War II on the U.S. economy, an economist used data from the

U.S. Census Bureau to produce the following Lorenz curves for the distribution of U.S. income in 1935 and in 1947:

$$

f(x)=x^{2.4} \quad \text { Lorenz curve for } 1935

$$

$$

g(x)=x^{1.6} \quad \text { Lorenz curve for } 1947

$$

Find the Gini index of income concentration for each Lorenz $z$ curve and interpret the results.

Bobby B.

University of North Texas

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

Using data from the U.S. Census Bureau, an economist produced the following Lorenz curves for the distribution of U.S. income in 1962 and in 1972 :

$$

f(x)=\frac{3}{10} x+\frac{7}{10} x^{2} \quad \text { Lorenz curve for } 1962

$$

$$

g(x)=\frac{1}{2} x+\frac{1}{2} x^{2} \quad \text { Lorenz curve for } 1972

$$

Find the Gini index of income concentration for each Lorenz

curve and interpret the results.

Wendi Z.

Numerade Educator

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

Lorenz curves also can provide a relative measure of the distribution of a country's total assets. Using data in a report by the U.S. Congressional Joint Economic Committee, an economist produced the following Lorenz curves for the distribution of total U.S. assets in 1963 and in 1983:

$$

f(x)=x^{10} \quad \text { Lorenz curve for } 1963

$$

$$

g(x)=x^{12} \quad \text { Lorenz curve for } 1983

$$

Find the Gini index of income concentration for each Lorenz curve and interpret the results.

Bobby B.

University of North Texas

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

The government of a small country is planning sweeping changes in the tax structure in order to provide a more equitable distribution of income. The Lorenz curves for the current income distribution and for the projected income distribution after enactment of the tax changes are as follows:

$$

f(x)=x^{2.3} \quad \text { Current Lorenz curve Projected Lorenz curve after changes in tax laws }

$$

$$

g(x)=0.4 x+0.6 x^{2}

$$

Bobby B.

University of North Texas

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

The data in the following table describe the distribution of wealth in a country:

$$

\begin{array}{ccccccc}

x & 0 & 0.20 & 0.40 & 0.60 & 0.80 & 1 \\

\hline y & 0 & 0.12 & 0.31 & 0.54 & 0.78 & 1

\end{array}

$$

(A) Use quadratic regression to find the equation of a Lorenz curve for the data.

(B) Use the regression equation and a numerical integration routine to approximate the Gini index of income concentration.

Bobby B.

University of North Texas

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

Refer to Problem $93 .$

(A) Use cubic regression to find the equation of a Lorenz curve for the data.

(B) Use the cubic regression equation you found in Part (A) and a numerical integration routine to approximate the Gini index of income concentration.

Bobby B.

University of North Texas

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

A yeast culture is growing at a rate of $W^{\prime}(t)=$ $0.3 e^{0.1 t}$ grams per hour. Find the area between the graph of $W^{\prime}$ and the $t$ axis over the interval [0,10] and interpret the results.

Bobby B.

University of North Texas

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

The instantaneous rate of change in demand for U.S. lumber since $1970(t=0)$, in billions of cubic feet per year, is given by

$$

Q^{\prime}(t)=12+0.006 t^{2} \quad 0 \leq t \leq 50

$$

Find the area between the graph of $Q^{\prime}$ and the $t$ axis over the interval $[35,40],$ and interpret the results.

Bobby B.

University of North Texas

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

A college language class was chosen for a learning experiment. Using a list of 50 words, the experiment measured the rate of vocabulary memorization at different times during a continuous 5 -hour study session. The average rate of learning for the entire class was inversely proportional to the time spent studying and was given approximately by

$$

V^{\prime}(t)=\frac{15}{t} \quad 1 \leq t \leq 5

$$

Find the area between the graph of $V^{\prime}$ and the $t$ axis over the interval $[2,4],$ and interpret the results.

Narayan H.

Numerade Educator

In the applications that follow, it is helpful to sketch graphs to get a clearer understanding of each problem and to interpret results. A graphing calculator will prove useful if you have one, but it is not necessary.

Repeat Problem 97 if $V^{\prime}(t)=13 / t^{1 / 2}$ and the interval is changed to [1,4] .

Narayan H.

Numerade Educator