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According to a certain estimate, the depth N(t), in cm, of water in a tank at t hours past 2 a.m. is given by N(t)=-20(t-5)^2+500 for all t from 0 to 10 hours, inclusive. According to this estimate, at what time does the tank's depth reach its maximum?
A) 5:30
B) 7:00
C) 7:30
D) 8:00
E) 9:00
My dilemma:
1) I understand that the equation is meant to equal the maximum depth at a certain value of t. How does one test values of t from 0 to 10 in less than 2 minutes?? Is there a quicker way to solve this?
2) If the answer to 1) is "when t-5=0" then how does one conclude that 500 is the target depth? For example, why could it not be 420 when t=7?
3)Is there something inherent in these types of questions that signals a given term in the formula (in this case, the +500) is the target value, even when the question doesn't specifically say so?
-L
A) 5:30
B) 7:00
C) 7:30
D) 8:00
E) 9:00
My dilemma:
1) I understand that the equation is meant to equal the maximum depth at a certain value of t. How does one test values of t from 0 to 10 in less than 2 minutes?? Is there a quicker way to solve this?
2) If the answer to 1) is "when t-5=0" then how does one conclude that 500 is the target depth? For example, why could it not be 420 when t=7?
3)Is there something inherent in these types of questions that signals a given term in the formula (in this case, the +500) is the target value, even when the question doesn't specifically say so?
-L
