x is a positive number of hours f(x) = 25 Using a quick graph, we find f(6.2108) = 25 (that's given, f itself doesn't matter) Since x is the number of hours, if the starting hour is 9 AM, at what time (hour and minute) will f(x) = 25? I would do 9 AM + 6 hours = 15 = 3 PM. Then 0.2108 * 60 = 12.648 minutes, so f(x) = 25 at 3:12 PM. My teacher marked me wrong because he rounded to 3:13 PM. The problem said specifically "at what time (hour and minute) will f(x) = 25" - it didn't say "at the beginning of what minute" or "closest to what minute" or anything of the sort. My score doesn't bother me - what bothers me is my teacher marking me wrong when I'm sure I'm not wrong. Here's further reasoning: He still stays the answer is 3:13 PM, his stance being "you should round." Who's right?

There's no justification for rounding here. For instance, clocks that are accurate to within 1 tenth of a second (or whatever) would always be half a second off if they "rounded to the nearest whole second" or something strange like that. There is absolutely no reason why you'd round to the nearest minute, either. If it's 3:12 and 55 seconds, you still say it's still 3:12, and "rounding" would just make half a minute off compared to the way the rest of the world tells time.

This is a case where, if unspecified, rounding is completely unjustified.

Quote: Original post by cowsarenotevil
There's no justification for rounding here. For instance, clocks that are accurate to within 1 tenth of a second (or whatever) would always be half a second off if they "rounded to the nearest whole second" or something strange like that. There is absolutely no reason why you'd round to the nearest minute, either.

This is a case where, if unspecified, rounding is completely unjustified.

Oh, excellent example. I'll present that to him, perhaps he'll change his mind. I doubt it, though. I'm going to find the director of math and talk to her.

I revised my post slightly while you're replying, if you didn't see it; I think it's slightly more convincing.

Quote: Original post by cowsarenotevil
I revised my post slightly while you're replying, if you didn't see it; I think it's slightly more convincing.

I just saw it. Once again, thanks. I don't like teachers like this :( Now I have to find time to talk to the director of the math department.

Some teachers are just awful, and get something into their head and regardless of technical correctness will mark you wrong. Some professors will say to you, "I write y' instead of dy/dx and GOD HELP YOU IF YOU DON'T DO THE SAME" even if you're perfectly in the right to write y'.

In other words: don't waste the energy worrying. You're in the right, he's a douchebag, and there's nothing you can do about it.

Quote: Original post by nullsquared
x is a positive number of hours

f(x) = 25

Using a quick graph, we find

f(6.2108) = 25

(that's given, f itself doesn't matter)

The MEANING of f matters!

For example, if you earn 3 dollars per hour, and you need 10 dollars total to buy something, how many hours should you work, 3 or 4? In this case, 3 isn't enough, so 4 is the correct answer.

On the other hand, if you are an employer who pays his employee said 3 dollars per minute and all you have is 10 dollars, then you can only pay him for 3 hours, not 4. So the answer depends on what f actually means. Makes sense?

Quote: Original post by DevFred
The MEANING of f matters!

For example, if you earn 3 dollars per hour, and you need 10 dollars total to buy something, how many hours should you work, 3 or 4? In this case, 3 isn't enough, so 4 is the correct answer.

You're right, but the question would be "how many hours do you need to work to earn at least 10 dollars?" because you get paid every hour, not continuously.

My function is not step-based, so this doesn't apply. The question wasn't "at the beginning of what minute will f(x) be at least 25?" in which case the answer would indeed be 3:13.

As others suggested, I would not worry about talking to the director. Some teachers are just like this. Just be happy it was one problem, and not an entire test (I have had that before). If you stir the pot on this one, you may find your teacher has a knee-jerk reaction which really puts you on the outs. There are only a couple more weeks left in the semester, so I would just let it go.

Quote: Original post by jackolantern1
As others suggested, I would not worry about talking to the director. Some teachers are just like this. Just be happy it was one problem, and not an entire test (I have had that before). If you stir the pot on this one, you may find your teacher has a knee-jerk reaction which really puts you on the outs. There are only a couple more weeks left in the semester, so I would just let it go.

Alright, I guess I'll let it be. Teachers like this really annoy me, though. Especially since he's also my APCS teacher (and in there it's practically as if he's in a relationship with Java). I think he has it out for me since I always get the top score of the class, yet I don't pay attention in class at all. USA high school education FTL