CALC BC #1
Storyboard Text
- Oh no, the vehicles are arriving at a rate of A(t)=450sqrt(sin(0.62t))What are we gonna do?!!
- The total number of vehicles that arrive at the plaza from 6 AM to 10 AM is just the integral of A(t).
- I think you're a moron
- I think there will be about 376 cars per hour
- There are many vehicles coming into the toll plaza..
- Actually I'm not a moron. We can take average value of rate at vehicles arrive using integral divided by interval.
- I see. I see. But isn't the rate at which vehicles arrive decreasing at 6 AM?
- They had to find out how many cars will arrive from 6 to 10 AM to evaluate how much money they will make.
- No, it is in fact increasing. if we take the derivative of the rate at which vehicles arrive, it is 149 vehicles/sec^2 meaning that its increasing
- Oh! I missed that. OMG there is a line forming where at any time t, there arecars in the line. What will the max amount of cars be?
- They made a bet to see how many cars would come through the toll per hour.
- Well when the rate of vehicles is 400 vehicles/hr, t is about 1.5.
- Which means that the line is greatest at about t=3.6 and there will be 71 vehicles!
- Then he proved that he was not a moron, but then Raj asked another question...
- Rambo clarifies his misunderstanding, but then Raj notices something...
- Raj is completely correct as if we take the integral of A(t) between 1.5 and 3.7, we get 71 vehicles.
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