According to a certain estimate, the depth N( t)

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?

1 Explanation

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Diego Scharifker

I find this answer given by the OG to be wrong, but I must be missing out on something.
I tried with t=9 and got that N(t)=180 which obviously is a positive, not a negative as the explanation states.

Any ideas?

When t = 5, the value of 20(t 5)2 + 500 is 500. For all values of t between 0 and 10, inclusive, except t = 5, the value of 20(t 5)2 is negative and 20(t 5)2 + 500 < 500. Therefore, the tank reaches its maximum depth 5 hours after 2:00 in the morning, which is 7:00 in the morning.

Nov 12, 2017 • Comment

Adam

Hi Diego,

The explanation states that for all values of t other than 5, the part "-20(t - 5)^2" is negative, not that the depth of the water "N(t)" is negative.

You (correctly) found N(9) = 180. The explanation is saying that when we plug 9 in, we get a negative value for the -20(9 - 5)^2 portion.

Nov 21, 2017 • Reply