Series

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• 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.

Thanks in advance
• 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.

Thanks in advance

Well if your P(t) is

$\displaystyle P(t) = 31 + \frac{30t^2+4t+1}{1-5t^2} + 20 e^{-.04t}(t+1)$

then $\displaystyle \lim_{t \to \infty} P(t) = 31 - 6 = 25$

Not sure how you think this is a series though?
• Apr 24th 2009, 04:08 PM
CalcGeek31
i felt that it might be a series going from 0 to infinity of a power series