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[M2] Integration Application Problem

Integration Application Problem

Please help to solve the following question



Thank you very much
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[隱藏]
What have you tried? Please show your workings.

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回覆 2# 風之男 的帖子

Here is working

but my answer is not correct


Thank you for helping
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The method looks good. Just a minor arithmetic error right after plugging N=160.

Also, it would be better to write an inequality (basically, > instead of =, doesn't change much), as the problem specifically said "exceed". Writing an equation in this instance is also fine.

Sidenote, natural log is written as ln (ell-en), not In (eye-en).

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See why do I insist on you to show your work? There is no need to go through the integration part again, as you already know how.

[ 本帖最後由 風之男 於 2022-3-19 10:21 PM 編輯 ]

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I have no idea either, I integrated dN/dt to become N = -80ln(t^2-16t+100) + 88 + 80ln100.
And then created an inequality 160 > -80ln[(t^2-16t+100)/100] + 88.
But I think I did something wrong because I got to 100e^(-9/10) > t^2-16t+100 and I don't know how to solve it.

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回覆 4# 風之男 的帖子

Thank you for your clear explanation.

May I know which part of my working is wrong?

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回覆 5# 風之男 的帖子

Sorry for disturbing again.

I have calculated this question for several times, I can't still find the answer.
Would you please help me to find the error/

The answer is 4.3 hours

[ 本帖最後由 luckjoe 於 2022-3-20 09:25 PM 編輯 ]

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引用:
原帖由 luckjoe 於 2022-3-20 07:45 PM 發表
Sorry for disturbing again.

I have calculated this question for several times, I can't still find the answer.
Would you please help me to find the error/

The answer is 4.3 hours
No worries. With your working, I'm not sure how you get 3.8176 - the line right after subbing N=160.
This question is really not the friendliest when it comes to actual arithmetic, so... yeah, I'd say scrap everything after subbing N=160, and try again. It's annoying and unproductive, but gotta suck it up.

If anything, your method is correct, so I commend your efforts.

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回覆 6# 風之男 的帖子

Thank you very much for your kind and rapid reply.

I will try it again

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引用:
原帖由 妙妙貓 於 2022-3-20 07:53 AM 發表
I have no idea either, I integrated dN/dt to become N = -80ln(t^2-16t+100) + 88 + 80ln100.
And then created an inequality 160 > -80ln[(t^2-16t+100)/100] + 88.
But I think I did something wrong bec ...
Look at the inequality carefully, isn't it just a quadratic inequality in t, just with a lot of annoying constants?
Hope you know how to solve a quadratic inequality.

Note: I didn't check if you actually arrive at the correct inequality. But based on experience you're quite careful with arithmetic, unlike me lol.

[ 本帖最後由 風之男 於 2022-3-20 09:38 PM 編輯 ]

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回覆 10# 風之男 的帖子

Thank you for your hint. I got the correct answer.

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