91Ó°ÊÓ

LORENZ CURVES In Exerises 47 through 50 , sketch the Lorenz curve \(y=L(x)\) and find the corresponding Gini index. \(L(x)=x^{1.2}\)

LORENZ CURVES In Exerises 47 through 50 , sketch the Lorenz curve \(y=L(x)\) and find the corresponding Gini index. \(L(x)=0.3 x^{2}+0.7 x\)

LORENZ CURVES In Exerises 47 through 50 , sketch the Lorenz curve \(y=L(x)\) and find the corresponding Gini index. \(L(x)=0.75 x^{2}+0.25 x\)

SURVIVAL AND RENEWAL In Exercises 51 through 54, an initial population \(P_{0}\) is given along with a renewal rate \(R(t)\) and a survival function \(S(t)\). In each case, use the given information to find the population at the end of the indicated term \(T\). \(P_{0}=75,000 ; R(t)=60 ; S(t)=e^{-0.09 t} ; t\) in months; term \(T=6\) months

SURVIVAL AND RENEWAL In Exercises 51 through 54, an initial population \(P_{0}\) is given along with a renewal rate \(R(t)\) and a survival function \(S(t)\). In each case, use the given information to find the population at the end of the indicated term \(T\). \(P_{0}=125,000 ; R(t)=250 ; S(t)=e^{-0.015 t} ; t\) in years; term \(T=5\) years

SURVIVAL AND RENEWAL In Exercises 51 through 54, an initial population \(P_{0}\) is given along with a renewal rate \(R(t)\) and a survival function \(S(t)\). In each case, use the given information to find the population at the end of the indicated term \(T\). \(P_{0}=100,000 ; R(t)=90 e^{0.1 t} ; S(t)=e^{-0.2 t} ; t\) in years; term \(T=10\) years

SURVIVAL AND RENEWAL In Exercises 51 through 54, an initial population \(P_{0}\) is given along with a renewal rate \(R(t)\) and a survival function \(S(t)\). In each case, use the given information to find the population at the end of the indicated term \(T\). \(P_{0}=200,000 ; R(t)=50 e^{0.12 t} ; S(t)=e^{-0.017 t} ; t\) in hours; term \(T=20\) hours

VOLUME OF SOLID OF REVOLUTION In Exercises 55 through 58 , find the volume of the solid of revolution formed by rotating the specified region \(R\) about the \(x\) axis. \(R\) is the region under the curve \(y=x^{2}+1\) from \(x=-1\) to \(x=2\).

VOLUME OF SOLID OF REVOLUTION In Exercises 55 through 58 , find the volume of the solid of revolution formed by rotating the specified region \(R\) about the \(x\) axis. \(R\) is the region under the curve \(y=e^{-x / 10}\) from \(x=0\) to \(x=10\).

VOLUME OF SOLID OF REVOLUTION In Exercises 55 through 58 , find the volume of the solid of revolution formed by rotating the specified region \(R\) about the \(x\) axis. \(R\) is the region under the curve \(y=\frac{1}{\sqrt{x}}\) from \(x=1\) to \(x=3\).