Bacterial Population: A bacterial colony is estimated to have a population of
P(t)=(24t+10)/(t^2+1)
Million t hours after the introduction or a toxin.
At what rate is the population changing in 1 hour after the toxin is introduced (t=1)? Is the population increasing or decreasing at this time?
At what time does the population begin to decline?
Is there a question here?
yes,
A Bacterial colony is estimated to have a population of million t hours after the introduction of a toxin
(a) At what rate is the population changing during 1 hr after the toxin is introduced (t=1)? Is the population increasing or decreasing @ this time?
(b) At what time does the population begin to decline?
Take the derivative
P' = dP/dt=24/(t^2+1) + ((24t+1)*(-1)(t^2+1)^-2 (2t)
a) for rate,put t=1 and compute. I get about 12-25=-13 check that. It is reducing (negative)
b) when does it decline is the same question as when is it max?
set P'=0, solve for t.
huh?
i'm new at this, please show me how to answer the problem. thanks
thank you for this, can you just please explain in a little more detail how i would go about getting the answer t question b? thanks
You need to start with question a.
Redo the differentiation of a quotient:
d(u/v) = (u dv - v du)/v²
using
u=24t+10
v=t^2+1
If you cannot do this part, backtrack on your notes to make sure you can do it. Otherwise you will have a difficulty doing other exercises.