Rounding in Physical Applications of Calculus (1 Viewer)

[ChrisChrisau]

Hi all!

When converting a decimal to a time in physical applications of calculus, do we round up or down?

For example, say your answer is 2.885 years (where year 0 = 2008), but the question wants the answer as a year and months. So we convert the 0.885years to a month and we get 10.6 months.

My question is, does this then go down as October or November? The event will take place in October, but normal rounding rules would bring it up to November.

Thanks!

 

[emmcyclopedia]

I suppose it would depend on how the question was worded.

If it said to the nearest month, then you would say 2 years and 11 months - like we usually round off any number.

If it asked the date, or in what month would it occur,
you'd say October (or whatever it was 2 years and 10.6 months later...)

hope that answers your question =]

 

[Zak Ambrose]

haha. well i did this paper today, 2007 if im not mistaken?
is was all in the wording of the Q. however i dont know if i got it right yet so i will wait until i post my help.

 

[scardizzle]

if the the question asks for the amount of time needed to reach a certain requirement you need to round up. For instance, i'll use loan repayments as an example,if the question asks what is John's monthly repayment required to pay off his loan or something similar you have to round up otherwise he will not reach the amount he owes

 

[boxhunter91]

haha. well i did this paper today, 2007 if im not mistaken?
is was all in the wording of the Q. however i dont know if i got it right yet so i will wait until i post my help.

The Answer was November 2010. I just done the paper. Actually quite difficult then other papers. You should always use exact values. Never round nothing unless asked.

 

[Zak Ambrose]

The Answer was November 2010. I just done the paper. Actually quite difficult then other papers. You should always use exact values. Never round nothing unless asked.

it was far more difficult than 2008! 2008 was far to easy.

 

[cutemouse]

For instance, i'll use loan repayments as an example,if the question asks what is John's monthly repayment required to pay off his loan or something similar you have to round up otherwise he will not reach the amount he owes

That's in series. I haven't encountered such an example in Applications of Calculus to the Physical world.

However for instance, if you have t=22.18 years, this would occur in the 23rd year. Something you need to be aware of if the question asks it.

 

[Zak Ambrose]

now. i have an issue with this question.
it is Q8(a) from the 2007 HSC.
specifically the issue is in part (ii).

the question says "According to the model, during which month and year will the number of mobile phones in use first exceed 4000 million?"
which is fine.

we find t = 2.88.....
which means the 2nd year 10th month

now we would USUALLY round up. by the question states "During which month and year will the number of mobile phones in use first exceed 4000 million?"

which means that during the 10th month, October, we find that N moves from N<4000 to N>4000. which means that N "first exceeds" 4000 "during" the 10th month.

so to me, the answer is October 2010. NOT November 2010 like this HSC Success book says.


if anyone thinks my working is wrong please correct, i dont want to sit the exam not being able to read the question

 

[cutemouse]

we find t = 2.88.....
which means the 2nd year 10th month

Uhh, t=2.88 years means that it occurs in the 3rd year. Towards the end of the 3rd year actually. ie. in November (11th month) in the 3rd year.

This is exactly what I was getting at in my previous post... Did you read it? -_-;

 

[Zak Ambrose]

Uhh, t=2.88 years means that it occurs in the 3rd year. Towards the end of the 3rd year actually. ie. in November (11th month) in the 3rd year.

This is exactly what I was getting at in my previous post... Did you read it? -_-;

yes i see where you are coming from.
2008 - 1st year
2009 - 2nd year
2010 - 3rd year

but my point still remains that 4000mil was reached after 2.88 [2years 10months] years.... which is October 2010.

what makes you say it occurs in November and not October?

 

[boxhunter91]

2.88 years = 34.56 months. Which is 35 Months Which is November 2010. With these sorts of question you always go to the next highest number. Its like series/sequences questions.

 

[Zak Ambrose]

2.88 years = 34.56 months. Which is 35 Months Which is November 2010. With these sorts of question you always go to the next highest number. Its like series/sequences questions.

i know that you should round up normally. but the wording of the question makes me think otherwise.
usually the question would ask AFTER [or by. etc] what month are there 4000mil phones.

but this Q asking DURING which month does N reach 4000mil.
and you cannot argue that N reaches 4000 in November because it doesn't, it reaches 4000 during october.

does N reach 4000 by november, yes. does it reach 4000 during november, no.

again, i realise you traditionally round up. but not in this case i believe.

pleased read the question again. i hope im right after all this ranting.

 

[cutemouse]

what makes you say it occurs in November and not October?

t=2.88 years = 2 years + 0.88 of a year.

0.88 *12 = 10.56 , which is the 11th month.

So it occurs in 11th month of the third year.

2.88 years = 34.56 months. Which is 35 Months Which is November 2010. With these sorts of question you always go to the next highest number. Its like series/sequences questions.

There is logic behind it it too. As I said if it takes 34.56 months to occur, then it occurs in the 35th month.

Say for instance, that it takes t=0.1 month(s) for something to occur. This occurs in the 1st month.

 

[cutemouse]

and you cannot argue that N reaches 4000 in November because it doesn't

Umm, yes it does -- You're wrong and SuccessOne is correct, as usual.

 

[Zak Ambrose]

t=2.88 years = 2 years + 0.88 of a year.

0.88 *12 = 10.56 , which is the 11th month.

So it occurs in 11th month of the third year.



There is logic behind it it too. As I said if it takes 34.56 months to occur, then it occurs in the 35th month.

Say for instance, that it takes t=0.1 month(s) for something to occur. This occurs in the 1st month.

ah! THANK YOU! i was waiting for some proof rather than "you just round up."
so i should have treated January as the 0th month, and december as the 11th.

• 0 < January <1/12
• 1/12< February < 2/12
• 2/12 < March < 3/12
• 3/12 < April < 4/12
• 4/12 < May < 5/12
• 5/12 < June < 6/12
• 6/12 < July < 7/12
• 7/12 < August < 8/12
• 8/12 < September < 9/12
• 9/12 < October < 10/12
• 10/12 < November < 11/12 [N=4000 occurs in November, the "10th" month]
• 11/12 < December < 12/12
  
  
  today's math study is DONE

 

[cutemouse]

November is not the "10th" month, it's the 11th month.

If something takes 2 years and 11 months to occur then it occurs in November, which is the 11th month of the year.

Geez, not that hard to understand: 2 whole years + 11 months occurs in 11th month of third year.

 

[ChrisChrisau]

ah! THANK YOU! i was waiting for some proof rather than "you just round up."
so i should have treated January as the 0th month, and december as the 11th.

• 0 < January <1/12
• 1/12< February < 2/12
• 2/12 < March < 3/12
• 3/12 < April < 4/12
• 4/12 < May < 5/12
• 5/12 < June < 6/12
• 6/12 < July < 7/12
• 7/12 < August < 8/12
• 8/12 < September < 9/12
• 9/12 < October < 10/12
• 10/12 < November < 11/12 [N=4000 occurs in November, the "10th" month]
• 11/12 < December < 12/12
  
  
  today's math study is DONE

Ah! I was on the exact same thought train as you! That helps me understand

Thanks for all the replies ! (Sorry for the late reply - I forgot to subscribe to this thread )