After declining between 1940 and 1980, the number of multigenerational American households has been increasing since 1980. The function h(x) = 0.012x2 − 0.583x + 35.727

Question

can be used to estimate the number of multigenerational households in the United States, in millions,

x years after 1940 (Source: Pew Research Center). Use this function to determine:

(a) In what year were there 40 million multigenerational households?

(b) In what year were there 55 million multigenerational households?

Answer 1

h(x) = .012x^2 -.538x + 35.727

it reaches 40 million when

40= 012x^2 -.538x +34.727

.012x^2 -.538x -5.273 = 0

use the quadratic formula to find x = the years after 1940

x= -b/2a +/-(1/2a)sqr(b^2-4ac), where a=.012, b=-.538, c=-5.273

there were 55 million when

55 =.012x^2 -.538x +34.727

0.12x^2 -.538x - 20.273 = 0

use the quadratic formula to solve for x= number of years since 1940