Question: ADVERTISING A company manufactures a "thin" DVD burner kit that can be plugged into personal computers. The marketing manager determines that \(t\) weeks after an advertising campaign begins, \(P(t)\) percent of the potential market is aware of the burners, where

\[P(t)=100\left[\frac{t^{2}+5 t+5}{t^{2}+10 t+30}\right]\]

1. At what rate is the market percentage \(P(t)\) changing with respect to time after 5 weeks? Is the percentage increasing or decreasing at this time?
2. What happens to the percentage \(P(t)\) in the "long run"; that is, as \(t \rightarrow+\infty\) ? What happens to the rate of change of \(P(t)\) as \(t \rightarrow+\infty\) ?

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