1. ## 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 and let me know if you need to me to clarify anything...I'm new.

2. 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 $t = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Originally Posted by ghostbuster
He also said some answers might not be possible with my data(Las Vegas pop)
This will be for $P,t <0$

3. Yep, solve as a normal quadratic
Could you give me a little more info as how to do that Where would the 1,000,000 go?

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

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

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

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

Now $a = 53, b= 2218 , c= -987179$

5. So I put these into
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.

6. Originally Posted by ghostbuster
So I put these into
and this will give the year that the population will be at 1 million?
yep....

7. 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?

8. 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!

Otherwise yep put 0 instead of 1 million.

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