Can someone please help me with letter b The accompanying table provides data on the number of men aged 65 or older in the United States and the percentage of men aged 65 or older living below the poverty level.| Year | Men 65 years or older, \( m \) (millions) | Percentage below poverty level, \( p \) ||------|-------------------------------------|------------------------------------|| 1970 | 8.3 | 20.2 || 1980 | 10.3 | 11.1 || 1985 | 11.0 | 8.7 || 1990 | 12.6 | 7.8 || 1997 | 14.0 | 7.0 || 2000 | 14.4 | 7.5 |(a) Using time as the input, fill in the blanks to complete a linear model for the data set for the number of men 65 years or older in the United States. (Let \( x \) be the years since 1970. Round all numerical values to three decimal places.)\[ m(x) = 0.209x + 8.208 \]million is the number of men in the U.S. 65 years and older, where \( x \) is years since 1970, \( 0 \leq x \leq 30 \).Using time as the input, fill in the blanks to complete a quadratic model for the data set for the percentage of men age 65 or older below poverty level. (Let \( x \) be the years since 1970. Round all numerical values to three decimal places.)\[ p(x) = 0.022x^2 - 1.085x + 20.070 \]% is the percentage of men in the U.S. 65 years and older below poverty level, where \( x \) is years since 1970, \( 0 \leq x \leq 30 \).The total number of U.S. men of age 65 and older living below the poverty level is given by the function:\[ l(x) = m(x) \cdot \frac{p(x)}{100} \]million men.(b) Using the unrounded models above, how rapidly was the number of male senior citizens living below the poverty level changing in 1995 and

The rate of change of a quantity is given by the derivative of it. Suppose that the function f(x) denote the value of a quantity at a particular time x. Then the change in f(x) with respect to the time x is given by f'(x). The function that gives the number of senior citizens living below the poverty level is l(x)=m(x)·p(x)100 where m(x)=0.209x+8.208 and p(x)=0.022x2-1.085x+20.070. First find the function l(x)=m(x)·p(x)100. l(x)=m(x)·p(x)100=0.209x+8.2080.022x2-1.085x+20.07100=0.209x· 0.022x2+0.209x-1.085x+0.209x· 20.07+8.208· 0.022x2+8.208-1.085x+8.208(20.07)100=0.004598x3-0.046189x2-4.71105x+164.73456100=0.010.004598x3-0.046189x2-4.71105x+164.73456=0.01· 0.004598x3+0.01-0.046189x2+0.01-4.71105x+0.01· 164.73456=0.00004598x3-0.00046189x2-0.0471105x+1.6473456 Therefore l(x)=0.00004598x3-0.00046189x2-0.0471105x+1.6473456.The change in the number of senior citizens living below the poverty level is the derivative of the function l(x)=0.00004598x3-0.00046189x2-0.0471105x+1.6473456. Find l'(x). l'(x)=ddx0.00004598x3-0.00046189x2-0.0471105x+1.6473456=ddx0.00004598x3-ddx0.00046189x2-ddx0.0471105x+ddx1.6473456=30.00004598x2-20.00046189x-0.0471105+0=0.00013794x2-0.00092378x-0.0471105+0=0.00013794x2-0.00092378x-0.0471105 Therefore l'(x)=0.00013794x2-0.00092378x-0.0471105.Now, to find the increase in the number of senior citizens living below the poverty level in 1995, substitute x=25 (1995-1970=25) in l'(x)=0.00013794x2-0.00092378x-0.0471105 and simplify. l'(25)=0.00013794· 252-0.00092378· 25-0.0471105=252· 0.00013794-0.0230945-0.0471105=252· 0.00013794-0.070205=0.0862125-0.070205=0.0160075 Therefore in three decimal place, the increase in the number of senior citizens living below the poverty level in 1995 is about 0.016 million men per year. Similarly substitute x=35 (2005-1970=35) in l'(x)=0.00013794x2-0.00092378x-0.0471105 and simplify to find the increase in the number of senior citizens living below the poverty level in 2005. l'(35)=0.00013794· 352-0.00092378· 35-0.0471105=352· 0.00013794-0.0323323-0.0471105=352· 0.00013794-0.0794428=0.1689765-0.0794428=0.0895337 Therefore in three decimal place, the increase in the number of senior citizens living below the poverty level in 2005 is about 0.089 million men per year.

Math

Advanced Math

(a) Using time as the input, fill in the blanks to complete a linear model for the data set for the number men 65 years or older in the United States. (Let x be the years since 1970. Round all numerical values to three decimal places.) m(x) = 0.209x + 8.208 million is the number of men in the U.S. 65 years and older , where x is years since 1970 OSXS 30. Using time as the input, fill in the blanks to complete a quadratic model for the data set for the percentage of men age 65 or older below poverty level. (Let x be the years since 1970. Round all numerical values to three decimal places.) p(x) =0.022x 2 1.085x + 20.070 % is the percentage of men in the U.S. 65 years and older below poverty level where x is years since 1970 v , 0 s xs 30 The total number of U.S. men of age 65 and older living below the poverty level is given by the function /(x) = m(x) · p(x) / 100 million men. (b) Using the unrounded models above, how rapidly was the number of male senior citizens living below the poverty level changing in 1995 and in 2005? (Round your answer to three decimal places.) 1995 1.601 X million men per year 2005 2.123 x million men per year

(a) Using time as the input, fill in the blanks to complete a linear model for the data set for the number men 65 years or older in the United States. (Let x be the years since 1970. Round all numerical values to three decimal places.) m(x) = 0.209x + 8.208 million is the number of men in the U.S. 65 years and older , where x is years since 1970 OSXS 30. Using time as the input, fill in the blanks to complete a quadratic model for the data set for the percentage of men age 65 or older below poverty level. (Let x be the years since 1970. Round all numerical values to three decimal places.) p(x) =0.022x 2 1.085x + 20.070 % is the percentage of men in the U.S. 65 years and older below poverty level where x is years since 1970 v , 0 s xs 30 The total number of U.S. men of age 65 and older living below the poverty level is given by the function /(x) = m(x) · p(x) / 100 million men. (b) Using the unrounded models above, how rapidly was the number of male senior citizens living below the poverty level changing in 1995 and in 2005? (Round your answer to three decimal places.) 1995 1.601 X million men per year 2005 2.123 x million men per year

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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