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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?
  • a)
    32
  • b)
    30
  • c)
    24
  • d)
    14
  • e)
    0
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The number of passengers on a certain bus at any given time is given b...
The bus will carry its greatest passenger load when P is at its maximum value. If P = -2(S – 4)2 + 32, the maximum value of P is 32 because (S – 4)2 will never be negat ive, so the expression -2(S – 4)2 will never be positive. The maximum value for P will occur when -2(S – 4)2 = 0, i.e. when S = 4. 
The question asks for the number of passengers two stops after the bus reaches its greatest passenger load, i.e. after 6 stops (S = 6).
P = -2(6 – 4)2 + 32
P = -2(2)2 + 32
P = -8 + 32
P = 24
Alternat ively, the maximum value for P can be found by building a table, as follows:


The maximum value for P occurs when S = 4. Thus, two stops later at S = 6, P = 24.
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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 itsroute. If the bus begins its route with no passengers, how many passengers will be on the bus two stops afterthe stop where it has its greatest number of passengers?a)32b)30c)24d)14e)0Correct answer is option 'C'. Can you explain this answer?
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