SOLUTION: 2. The population of a certain strain of bacteria is represented by the function g(t) = t^4+6t^3-t^2-6t, where t is in hours. How many bacteria will there be after 3 hours? How man

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 2. The population of a certain strain of bacteria is represented by the function g(t) = t^4+6t^3-t^2-6t, where t is in hours. How many bacteria will there be after 3 hours? How man      Log On


   

Question 1188373: 2. The population of a certain strain of bacteria is represented by the function g(t) = t^4+6t^3-t^2-6t, where t is in hours. How many bacteria will there be after 3 hours? How many hours will the population of the bacteria become 2520?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


You will learn nothing from this if we simply give you the answers....

First question: evaluate g(3)

Second question: Find t for which g(t)=2520

The first question can be answered with pencil and paper, since it is just plugging in numbers and doing calculations.

The second question solved algebraically means solving a 4th degree polynomial equation, which in general is very difficult. I wouldn't bother....

Both questions can be answered quickly and easily using a graphing calculator.

Try it...

Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.

t^4 + 6t^3 - t^2 - 6t = factor by grouping = t^3*(t+6) - t*(t+6) = (t^3 - t)*(t+6) = t*(t^2-1)*(t+6).


5220 is divisible by 2 and by 3 (via the sum of digits), so it is divisible by 6.


So, try t = 6, and you will see that  6*(6^2-1)*(6+6) = 6*35*12 = 2520.


So, t= 6 hours is one of possible solutions.