The problem should read as follows:
According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t-5)²+500 for 0≤t≤10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum?
a) 5:30 b) 7:00 c) 7:30 d) 8:00 e)9:00
Depth = 500 -
20(t-5)².
To MAXIMIZE the depth, we must MINIMIZE the value in red.
Since the square of a value cannot be negative, (t-5)² ≥ 0.
Thus, the value in red will be minimized when (t-5)² = 0.
Since (t-5)² = 0 when t=5, the depth will be at its maximum 5 hours after 2am:
2am + 5 hours = 7am.
The correct answer is
B.
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