population decrease in bacteria colony after intro of toxin

yanarains

New member
Joined
Sep 27, 2007
Messages
25
A bacterial colony is estimated to have a population of

P(t) = 14t+4/t^2+1 million t hours after the introduction of a toxin.

At what time does the population begin to decrease.

Could someone please help me finish this problem:

p(t)= (t^2+1) x 14 - (14t+4) x 2t = -14t^2-8t+14 / (t^2+1)

To find out when the population begins to decrease, what is my next step? My book explains that the next step is to factor the numerator which in this case could factor out to be -2(7t^2+4t-7)(?).
Well that is about how far I get, I can't seem to figure out how to factor out this problem I guess.

help please and thankyou!
 
in future, please use proper grouping symbols to make your function clear to those that read it.

P(t) = (14t + 4)/(t^2 + 1)

P'(t) = -2(7t^2 + 4t - 7)/(t^2 + 1)^2

7 - 4t - 7t^2 will not factor over the rationals, use the quadratic formula ...

t = [sqrt(53) - 2]/7
 
Top