# Use a quadractic regression equation to predict population.

• Mar 31st 2010, 01:00 PM
ghostbuster
Use a quadractic regression equation to predict population.
I was given the population of Las Vegas for every 10 years starting at 1900 and ending in 1990. From these 10 data points I created a table and Graph with my Ti-83.

I found the quadratic regression equation. P =population t=time since 1900

P(t)=53.4804t^2-2217.5496t+12820.6454

I also found the x intercepts and the vertex.
X=34.5202
X=6.9445

The vertex
X=20.7324
Y=12820.6454

Now this is the part where I am stuck. My teacher wants me use to use the above information to determine when will (was) the population of Las Vegas be 1 million people, when was (will) the population be zero? He also said some answers might not be possible with my data(Las Vegas pop)

So I guess that I need to substitute 1 million into P of my equation and solve for t. Is this right ? If so how would I go about that? or is it something else?

I appreciate any help http://www.sosmath.com/CBB/images/smiles/icon_lol.gif and let me know if you need to me to clarify anything...I'm new.
• Mar 31st 2010, 01:43 PM
pickslides
Quote:

Originally Posted by ghostbuster

So I guess that I need to substitute 1 million into P of my equation and solve for t. Is this right ? If so how would I go about that? or is it something else?

Yep, solve as a normal quadratic $\displaystyle t = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Quote:

Originally Posted by ghostbuster
He also said some answers might not be possible with my data(Las Vegas pop)

This will be for $\displaystyle P,t <0$
• Mar 31st 2010, 02:50 PM
ghostbuster
Quote:
Could you give me a little more info as how to do that(Nod) Where would the 1,000,000 go?
• Mar 31st 2010, 03:33 PM
pickslides
$\displaystyle P(t)=53.4804t^2-2217.5496t+12820.6454$

$\displaystyle 1000000=53.4804t^2-2217.5496t+12820.6454$

$\displaystyle 1000000=53.4804t^2-2218t+12821$

$\displaystyle 0=53t^2-2218t-987179$

Now $\displaystyle a = 53, b= 2218 , c= -987179$
• Mar 31st 2010, 04:18 PM
ghostbuster

So I put these into http://www.mathhelpforum.com/math-he...f94c47dd-1.gif
and this will give the year that the population will be at 1 million?

Thanks for the help....I've haven't been in a math class for a couple of years.(Rofl)
• Mar 31st 2010, 04:28 PM
pickslides
Quote:

Originally Posted by ghostbuster
So I put these into http://www.mathhelpforum.com/math-he...f94c47dd-1.gif
and this will give the year that the population will be at 1 million?

yep....(Happy)
• Mar 31st 2010, 04:45 PM
ghostbuster
Quote:

when was (will) the population be zero?
]
is this possible?...do I just do the same thing but put in a zero instead of 1 million?
• Mar 31st 2010, 05:04 PM
pickslides
Quote:

Originally Posted by ghostbuster
]
is this possible?...do I just do the same thing but put in a zero instead of 1 million?

Could be 0 if gambling became prohibited! (Rofl)

Otherwise yep put 0 instead of 1 million.

Note that if $\displaystyle b^2-4ac < 0$ there will be no solutions.