# Thread: Find the Year

1. ## Find the Year

According to data from the U.S. Census Bureau, the population P of Cleveland, Ohio (in thousands) in year x can be approximated by the equation P = .08x^2 - 13.08x + 927 , where x = 0 corresponds to the year 1950. In what year (in the past) was the population about 804, 200?

2. Originally Posted by emfn96
According to data from the U.S. Census Bureau, the population P of Cleveland, Ohio (in thousands) in year x can be approximated by the equation P = .08x^2 - 13.08x + 927 , where x = 0 corresponds to the year 1950. In what year (in the past) was the population about 804, 200?
Set $.08(x)^2 - 13.08(x) + 927 = 804,200$

$\Rightarrow .08(x)^2 - 13.08(x) - 803273 = 0$

Then use the quadratic formula to find $x,$ the number of years after $1950$ this event occurred.

Note that:

$a=.08$

$b=-13.08$

$c=- 803273$

$\frac{-b +/- \sqrt{b^2 - 4ac}}{2a}$

Now plug and chug, as they say.

3. ## Quadratic Formula

Originally Posted by Anonymous1
Set $.08(x)^2 - 13.08(x) + 927 = 804,200$

$\Rightarrow .08(x)^2 - 13.08(x) - 803273 = 0$

Then use the quadratic formula to find $x,$ the number of years after $1950$ this event occurred.

Note that:

$a=.08$

$b=-13.08$

$c=- 803273$

$\frac{-b +/- \sqrt{b^2 - 4ac}}{2a}$

Now plug and chug, as they say.
I had no clue that the quadratic formula was needed to find the answer.

4. It's not "required" but you did recognise that this is a quadratic equation, didn't you?

5. it is straight forward quadractic equation.