fb0fa1a1ecb5b0 2017-10-2 01:49 PM

答案1用了代入，答案2用了整公式。我想問問哪個寫法才對？

ppresent 2017-10-2 10:23 PM

"Express A in the form of B" is usually used when you can do some algebra to A to make it in the form of B, such as "Express [img]https://latex.codecogs.com/gif.latex?3x%5E2+6x+3[/img] in the form of [img]https://latex.codecogs.com/gif.latex?a%28x+b%29%5E2[/img]".

I think it is not a good use in this case because it is not through some algebraic operations you make P in the form [img]https://latex.codecogs.com/gif.latex?ae%5E%7Bbt%7D[/img]. In fact, you write [img]https://latex.codecogs.com/gif.latex?P%3Dae%5E%7Bbt%7D[/img] directly (expressing P as [img]https://latex.codecogs.com/gif.latex?ae%5E%7Bbt%7D[/img]) and then find a & b by plugging in inputs of t & P.

Get back to your question of which answer should be correct. As the question mentions that the population is increasing by 3% per year, so I guess that means the population after t years would be 3% more than the population of last year (after t-1 years, t >= 1), i.e. [img]https://latex.codecogs.com/gif.latex?%5Cfrac%20%7Bae%5E%7Bbt%7D%7D%7Bae%5E%7Bb%28t-1%29%7D%7D%20%3D%201.03[/img]

and we have

[img]https://latex.codecogs.com/gif.latex?%5Cbegin%20%7Barray%7D%20%7Brcl%7D%20e%5Eb%26%3D%261.03%20%5C%5C%20b%20%26%20%3D%20%26%20%5Cln%201.03%20%5Cend%20%7Barray%7D[/img]

Hence your friend's answer should be correct.

[[i] 本帖最後由 ppresent 於 2017-10-2 11:22 PM 編輯 [/i]]

I think it is not a good use in this case because it is not through some algebraic operations you make P in the form [img]https://latex.codecogs.com/gif.latex?ae%5E%7Bbt%7D[/img]. In fact, you write [img]https://latex.codecogs.com/gif.latex?P%3Dae%5E%7Bbt%7D[/img] directly (expressing P as [img]https://latex.codecogs.com/gif.latex?ae%5E%7Bbt%7D[/img]) and then find a & b by plugging in inputs of t & P.

Get back to your question of which answer should be correct. As the question mentions that the population is increasing by 3% per year, so I guess that means the population after t years would be 3% more than the population of last year (after t-1 years, t >= 1), i.e. [img]https://latex.codecogs.com/gif.latex?%5Cfrac%20%7Bae%5E%7Bbt%7D%7D%7Bae%5E%7Bb%28t-1%29%7D%7D%20%3D%201.03[/img]

and we have

[img]https://latex.codecogs.com/gif.latex?%5Cbegin%20%7Barray%7D%20%7Brcl%7D%20e%5Eb%26%3D%261.03%20%5C%5C%20b%20%26%20%3D%20%26%20%5Cln%201.03%20%5Cend%20%7Barray%7D[/img]

Hence your friend's answer should be correct.

[[i] 本帖最後由 ppresent 於 2017-10-2 11:22 PM 編輯 [/i]]

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