The following spreadsheet shows the projected 2020 and 2030 U.S. male and female population in various age groups, as well as per capita incomes. Give a single matrix formula that expresses the total income in 2030. (Take D to be the total income, take N to be the income per person, and take F and M to be, respectively, the female and male populations in 2030.) D = NF + M D = NFM D = NF - M D = N(F + M) D = N(F - M) Compute its value, rounded to two significant digits. $ trillion Solution Total income in 2030 is D = N(F + M) Since, total income of all the people is equal to total number of people times income per person. Now in 2030, Between Age Group 15 to 24: Per capita income i.e, income per person in this age group = $14000 Total number of people (F + M) = (25 + 26) = 51 million D = N(F + M) = (14000)(51) = $ 714000 million = $ 7.14 trillion (since 1000 million = 1 billion and 1000 billion = 1 trillion) Between Age Group 25 to 44: Per capita income i.e, income per person in this age group = $42000 Total number of people (F + M) = (45 + 46) = 91 million D = N(F + M) = (42000)(91) = $ 3822000 million = $ 38.22 trillion Between Age Group 45 to 64: Per capita income i.e, income per person in this age group = $48000 Total number of people (F + M) = (42 + 41) = 83 million D = N(F + M) = (48000)(83) = $ 3984000 million = $ 39.84 trillion Between Age Group 65 to 84: Per capita income i.e, income per person in this age group = $29000 Total number of people (F + M) = (40 + 31) = 71 million D = N(F + M) = (29000)(71) = $ 2059000 million = $ 20.59 trillion Hence total income of all people = $ (7.14 + 38.22 + 39.84 + 20. 59) = $ 105.79 trillion..

1. The following spreadsheet shows the projected 2020 and 2030 U.S. male and female population
in various age groups, as well as per capita incomes. Give a single matrix formula that expresses
the total income in 2030. (Take D to be the total income, take N to be the income per person, and
take F and M to be, respectively, the female and male populations in 2030.) D = NF + M D =
NFM D = NF - M D = N(F + M) D = N(F - M) Compute its value, rounded to two significant
digits. $ trillion
Solution
Total income in 2030 is D = N(F + M)
Since, total income of all the people is equal to total number of people times income per person.
Now in 2030,
Between Age Group 15 to 24:
Per capita income i.e, income per person in this age group = $14000
Total number of people (F + M) = (25 + 26) = 51 million
D = N(F + M) = (14000)(51) = $ 714000 million = $ 7.14 trillion (since 1000 million = 1 billion
and 1000 billion = 1 trillion)
Between Age Group 25 to 44:
Per capita income i.e, income per person in this age group = $42000
Total number of people (F + M) = (45 + 46) = 91 million
D = N(F + M) = (42000)(91) = $ 3822000 million = $ 38.22 trillion
Between Age Group 45 to 64:
Per capita income i.e, income per person in this age group = $48000
Total number of people (F + M) = (42 + 41) = 83 million
D = N(F + M) = (48000)(83) = $ 3984000 million = $ 39.84 trillion
Between Age Group 65 to 84:
Per capita income i.e, income per person in this age group = $29000
Total number of people (F + M) = (40 + 31) = 71 million
D = N(F + M) = (29000)(71) = $ 2059000 million = $ 20.59 trillion
Hence total income of all people = $ (7.14 + 38.22 + 39.84 + 20. 59) = $ 105.79 trillion.