Question: A traffic engineer monitors the rate at which cars enter the main highway during the afternoon rush hour. From her data she estimates that between 4:30 P.M. and 5:30 P.M. the rate \(R(t)\) at which cars enter the highway is given by the formula \(R(t)=100\left(1-0.0001 t^{2}\right)\) cars per minute, where \(t\) is the time (in minutes) since 4:30 P.M.

1. When does the peak traffic flow into the highway occur?
2. Estimate the number of cars that enter the highway during the rush hour.

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