Math help! If population is modelled by 12t+800t+40 000 (where t=0 in 2007)?

Question

what year will the population be 30 000?

And also, I need help completing the square where 3x^2 - 5 =22 and another question where b^2 +20b = -80 (in this question i need to find out what x and y equal as well)

I have a test coming up and i need help with this!
Thanks! Even help for one question will be greatly appreciated!

EDIT: thanks! it is 12t^2+800t+40000

But i still need help!

Answer 1

12t^2+800t+40 000 <-- Assumed you meant this
When t= 0, Population P = 40,000
In 2008 Population will be 12(1)^2 +800(1) +40000= 40,812
In 2010, P will be 12*3^2+800*3+40,000 = 42,508

You don't say what year you would like to know P

3x^2 -5x = 22 <-- Assumed you meant this
x^2-5x/3 = 22/3
x^2-5x/3 +25/9 = 22/3 +22/9
(x-5/3)^2 = 88/9
You can solve for x from here getting:
x-5/3 = +/- sqrt(88/9) = +/- 2sqrt(22)/3
x = 5/3 +/- 2sqrt(22)/3

b^2 +20b = -80
b^2 +20 b +100 = 100-80
(b+10)^2 = 20
b+10 = +/- sqrt(20) = +/- 2sqrt(5)
b = -10 +/- 2sqrt(5)
There is no x or y in this last problem

Answer 2

I think your equation is wrong....did you mean 12t^2 + 800t + 40000?