E(t) = rac{(t + 1)(t + 3)}{t + 1}
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- Thus, the probability is $oxed{\dfrac{42}{55}}$.Question: A bioinformatician models the expression level of a gene as a function $ E(t) = rac{t^2 + 4t + 3}{t + 1} $, where $ t $ represents time in hours after treatment. Simplify $ E(t) $ and determine $ \lim_{t o -1} E(t) $, if it exists.
- Solution: We begin by factoring the numerator:
- t^2 + 4t + 3 = (t + 1)(t + 3)
- For $ t
- e -1 $, we can cancel $ t + 1 $, giving:
- E(t) = t + 3 \quad ext{for } t
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