Question

The accompanying table gives the number of men 65 years or older in the united states and the percentage of men age 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, find 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) = million men

Answer 1

or linear model of the given information we need to write the equation of a line

taking the datas from year 1970 and 1980

since x be the year since 1970 so for 1970 x=0 and for 1980 x=10

now for 1970 population=8.3 and for 1980 it is 10.3

we need to write the equation using (0,8.3) and (10,10.3)

x=0 y=20.2

Using time as the input, find a quadratic model for the data set for the percentage of men age 65 or older below poverty level. (x is the years since 1970. Round all numerical values to three decimal places.)

p(x)=.022x^2-1.085x+20.070 % is the percentage of men in the U.S. of age 65 and older living below the poverty level x years after 1970, 0 ? x ? 30

b.Using time as the input, find a quadratic model for the data set for the percentage of men age 65 or older below poverty level. (x is the years since 1970. Round all numerical values to three decimal places.)

p(x)=.022x^2-1.085x+20.070 % is the percentage of men in the U.S. of age 65 and older living below the poverty level x years after 1970, 0 ? x ? 30

l(x) = m(x) � p(x) / 100

l(x)=(0.2x+8.3)*(.022x^2-1.085x+20.070)/100

for year 1990 x=1990-1970=20

l(x)=12.3*7.17/100=0.881

for year 2000

x=30

substituting x to the derived equation below, we have m = 0.2*30 + 8.3, the answer is 14.3 Million