Pre calculus 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^2-0.543x+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 40 million multigenerational households? Round to the nearest whole number please put the year as the answer

Answer 1

Substituting 40 in for h(x), 40=.012x^2-.543x+35.723. Moving 40 to the other side yields 0= .012x^2-.543x-4.277

Converting this equation to whole numbers as coefficients yields (12x^2-543x-4277)/1000 = 0

So the numerator =0, So 12x^2-543x-4277=0

Using quadratic formula on this,yields x=52.09205 (the positive side). Rounding this number to the nearest whole number = 52 makes the year at which the population as 40 million households, 1940+52 = 1992

Answer 2

You are given the function, and you are asked at what value of x is h(x) = 40. Therefore, substitute 40 for h(x) to get

40 = 0.012x^2 -0.543x + 35.723

Subtract 40 from both sides to get

0 = 0.012x^2 -0.543x -4.277

Now, use the quadratic equation to solve for x

x = [ 0.543 +/- sqrt{ (-.543)^2 - [ 4*(0.012)*(-4.277)] } ]/(2*0.012)

x = 52.09 or x = -6.84 You can reject the negative value.

Rounded to a whole number, there were 40 million multigenerational households 52 years after 1940, or in the year 1992.