in thomas calculus $1$ textbook 12th edition, in page $154$ question $26$, it says: ///The number of gallons of water in a tank, t minutes after the tank has started to drain is $Q(t)=200(30-t)^2$How fast is the water running out at the end of $10$ min?// and the solution guide says:

solution textbook

why $t=10$??? end of $10th$ minute is $11th$ minute, right? then why? i'm completely confused and i really need your help guys. thank you. :-*

  • $\begingroup$ is this actually a math question? $\endgroup$ – jameselmore Nov 18 '16 at 15:15
  • $\begingroup$ this question is in math book, i don't know. you tell me $\endgroup$ – Sarah Nov 18 '16 at 15:15
  • $\begingroup$ Oh I thought your question was about end of $10$th minute should be $t=11$ $\endgroup$ – jameselmore Nov 18 '16 at 15:17
  • $\begingroup$ isn't it math??? $\endgroup$ – Sarah Nov 18 '16 at 15:23
  • $\begingroup$ It's the same reason why we live in the 21st century even though all our year numbers start with the digits 20: the year 2000 occurred at the end of the 20th century, not the beginning. $\endgroup$ – David K Nov 18 '16 at 15:51

You start at $t=0$. At the end of the first minute, you are at $t=1$. At the end of the second minute, you are at $t=2$. In general, at the end of $n$ minutes, you are at $t=n$.

  • $\begingroup$ @Fleonard The right way to thank someone for an answer is to accept the answer (the checkmark) and upvote it (the up arrow). You can upvote more than one answer. $\endgroup$ – Ethan Bolker Nov 18 '16 at 15:30

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