SOLUTION: I am really having troubles with these word problems. an experimental drug is being tested on a bacteria colony. It is found that t days after treating the colony, the number N

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Question 762488: I am really having troubles with these word problems.
an experimental drug is being tested on a bacteria colony. It is found that t days after treating the colony, the number N of bacteria per cubic centimeter is given by the equation N = 20t^2 -220t - 558. How long until the colony is reduced to 1482 bacteria
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The question is the same as, what is t when N=1482 ?
You would have 20t%5E2-220t-558=1482 and solve for t.
Simplify the equation a bit:

20t%5E2-220t-2040=0
t%5E2-11t-102=0
Factorable...

highlight%28%28t-17%29%28t%2B6%29=0%29 and you are interested in only the highlight%28t=17%29.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

use the equation N+=+20t%5E2+-220t+-+558 and plug in N=1482 bacteria
1482+=+20t%5E2+-220t+-+558

+0=+20t%5E2+-220t+-+558-1482

+0=+20t%5E2+-220t+-+2040.....all terms divide by 20

+0=+20t%5E2%2F20+-220t%2F20+-+2040%2F20

+0=+t%5E2+-11t+-+102

t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

t+=+%28-%28-11%29+%2B-+sqrt%28+%28-11%29%5E2-4%2A1%2A%28-102%29%29%29%2F%282%2A1%29+

t+=+%2811+%2B-+sqrt%28121%2B408%29%29%2F2+
t+=+%2811+%2B-+sqrt%28529%29%29%2F2+
t+=+%2811+%2B-+23%29%2F2+......since we are looking for a time, we will find only positive value of t
t+=+%2811+%2B+23%29%2F2+
t+=+34%2F2+
t+=+17+ days until the colony is reduced to 1482 bacteria