Please Help! Quadratic Eqautions
posted by Nina .
The population of a town P(t)is modelled by the function P(t)=6t+110t+3000, where t is time in years. Note t=0 represents the years 2000.

Typo and what is the question 
Damon
Suspect you mean
P(t) = 6 t^2 + 110 t + 3000 
Please Help! Quadratic Eqautions 
Nina
oh i'm sorry. i left out that part.. the question is
When will the population reach 6000? 
Please Help! Quadratic Eqautions 
Nina
P(t) = 6 t^2 + 110 t + 3000

Please Help! Quadratic Eqautions 
Damon
where is it max and min or something?
If you do not know calculus, find vertex of parabola by completing the square
t^2 + 18.33 t + 500 = P/6
t^2 + 18.33 = P/6  500
t^2 + 18.33 + 84 = P/6 500 +84
(t+9.17)^2 = P/6  416
(t+9.17)^2 = (1/6)(p2496)
minimum at t = 9.17 and p = 2496
that is the year 2000  9.17 = 1991 
Please Help! Quadratic Eqautions 
Damon
oh, hang on

Please Help! Quadratic Eqautions 
Nina
The question doesn't state wheater it's a max or min
it'as grade 11 math
no I have not done calculus 
Please Help! Quadratic Eqautions 
Nina
oh ok

Please Help! Quadratic Eqautions 
Damon
6000 = 6 t^2 + 110 t + 3000
6 t^2 + 110 t = 3000
t^2 + 18.3 t  500 = 0
t = [ 18.3 +/sqrt(336+2000)]/2
t = [18.3 + sqrt(2336)]2
t = [18.3 + 48.3 ]/2
t = 15
so 2015 
Please Help! Quadratic Eqautions 
Nina
Thank you
Much Appreciated !! (Y):) 
Please Help! Quadratic Eqautions 
Nina
Honestly, although i appreciate this help
Is there any other way to do this problem. I think this is a little to advanced because i really don't understand it. 
Please Help! Quadratic Eqautions 
Nina
too*

Please Help! Quadratic Eqautions 
mathgeekdude
You can go Damon's way, or the graphing way/ comnpleting the square binomial way or you can go quadratic

Please Help! Quadratic Eqautions 
Steve
6 t^2 + 110 t + 3000
if you're starting to study quadratics, you have surely used the quadratic formula to find the roots.
As Damon showed,
t = [18.3 + 48.3 ]/2
or
t = 9.15 ± √24.14
You know the parabola is symmetric, and the vertex is midway between the roots. Note that the roots are equally spaced around t = 9.15
so, the vertex is at t = 9.15. That will be the min or max.
If none of this makes any sense, you just need to study the quadratic formula some more. There are lots of examples online, and surely some in your class materials. If all that still makes no sense, no written explanation will be any clearer; some inperson help will help clear things up.
Also, a visit to
http://rechneronline.de/functiongraphs
will let you play around with various formulas and see what happens when you change stuff.
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