Precalculus word problem

Question

After declining between 1940 and 1980, the number of multigenerational households has been increasing since 1980. The function h(x)=0.012x^2-0.593x+35.721 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

0.12x^2- 0.59*x + 35.721 = 50

120 x^2 - 590x + 35721 = 50000

120x^2 - 590x -14279 = 0

quadratic formula says x=13.64

1940+13.64 = 1953.64

So July 1973

Answer 2

h(x)=0.012x^2-0.593x+35.721; h(x) in 000,000

It seemed easier to use a calculator on this one rather than to solve it analytically. Put the function into your calculator with Y=. Evaluate the function, using the CALC button with VALUE at x = 40 (which is 1980 according to the calendar). Evaluate the function at x = 79, which is the year 2019. Keep going down if you are too high and up if you are too low and you will find that the function produces 50 between the 67th and 68th year, or 2007 to 2008. It seems definite that there were 50 million multigenerational households in country A in 2008.

Note we are given that the function is decreasing from 1940 to 1980 and increasing thereafter, so we should be sure to check what h(x) was in 1940, which is h(0) = 35.721 which is less than 50.

Given the coefficients of h(x), it seems that you were expected to use a calculator. It would be very tedious to solve analytically. If there is a specific method you were requested to use, please advise.