luckjoe

Please help to solve the following question



Thank you very much

風之男

What have you tried? Please show your workings.

luckjoe

Here is working

but my answer is not correct


Thank you for helping

風之男

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 ]

妙妙貓

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.

luckjoe

Thank you for your clear explanation.

May I know which part of my working is wrong?

luckjoe

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 ]

風之男

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.

luckjoe

Thank you very much for your kind and rapid reply.

I will try it again

風之男

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 ]

妙妙貓

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