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The number of passengers on a certain bus....

Expert replies
by ddm » Mon Aug 25, 2008 3:27 pm
The number of passengers on a certain bus at any given time is given by the equation
P = -2(S – 4)^2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, how many passengers will be on the bus two stops after the stop where it has its greatest number of passengers?


32
30
24
14
0

OA-C
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Source: — Problem Solving |

by kuroneko1313 » Mon Aug 25, 2008 3:58 pm
First we have to find the equation in which there are maximum numbers of passengers in the bus during certain numbers of stop.

P' = -2(2)(s-2)
= -4s + 16

Maximum number of passenger happens when P' = 0

0 = -4s + 16
s = 4

So maximum passenger is reached during the 4th stop.

The question's asking for two stops after the stop where it has its greatest number of passengers, i.e. during the 6th stop. So plug-in the number:

P = -2(6-2)^2 + 32
= -2(4) + 32
= 24

I hope that helps.
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