Precalculus word problem

Question

after declining between 1940 and 1980, the number of multigenerational households has been increasing since 1980. the function h(x)=0.012x²-0.543x+35.723 can be used to estimate the number of multigenerational households in country A, in millions, x years after 1940. in what year were there 50 million multigenerational households?

Answer 1

0.012x²-0.543x+35.723 = 50

12x^2 - 543x + 35723 = 50000

12x^2 - 543x - 14277 = 0

quadratic formula says x = 63.875946958827505

That would be 1940 + 63 = 2003 so the population of multi-generation households

was 50 million in late August 2003

Answer 2

For this problem, you substitute in 50 million for h(x) and solve for x. They said h(x) is in millions so you substitute in 50 for h(x). 50=0.012x²-0.543x+35.723. Then you can solve for x using the quadratic formula, -b +/- (Sqrt(b^2-4ac))/2a. When I did this I found the value 63.876. That means that 64 years after 1940 there are 50 million homes. So in 2009, there were 50 million homes. Hope that helps.