# Series

• Apr 24th 2009, 03:54 PM
CalcGeek31
Series
In an experiment, a biologist introduces a toxin into a bacterial colony and then measures the effect on the population of the colony. Suppose that at time t(in minutes) the population is given by P(t) = 31 + (30t^2 +4t+1)/(1-5t^2) + 20e^(-.04t)(t+1) measured in thousands. What will the population be as t approaches infinity (measured in thousands)?

I think this is a Series problem, help needed.

• Apr 24th 2009, 04:01 PM
Jester
Quote:

Originally Posted by CalcGeek31
In an experiment, a biologist introduces a toxin into a bacterial colony and then measures the effect on the population of the colony. Suppose that at time t(in minutes) the population is given by P(t) = 31 + (30t^2 +4t+1)/(1-5t^2) + 20e^(-.04t)(t+1) measured in thousands. What will the population be as t approaches infinity (measured in thousands)?

I think this is a Series problem, help needed.

$P(t) = 31 + \frac{30t^2+4t+1}{1-5t^2} + 20 e^{-.04t}(t+1)$
then $\lim_{t \to \infty} P(t) = 31 - 6 = 25$