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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, what is the value of S when the bus has its greatest number of passengers?
a) 9
b) 6
c) 4
d) 2
e) 1
a) 9
b) 6
c) 4
d) 2
e) 1
14 Feb 2018, 07:18
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nekiwa07
\(P = –2(S – 4)^2 + 32\):
\(–2(S – 4)^2 = (-2)*(square \ of \ a \ number)= (negative)*(non-negative) = (non-positive)\). So, this term is negative or 0.
Therefore, P, the number of passengers, will be maximized when \(–2(S – 4)^2\) is 0. In this case \(P_{max} = –2(S – 4)^2 + 32= 0+32=32\). For, \(–2(S – 4)^2\) to be 0, S should be 4.
Answer: C.
Hope it's clear.
