F.4 Exponential Function

👨🏻‍🏫 學術台數學

知識就是力量

2009-11-07 6:29 am

Let f(x) = 2(3^x). Determine whether the value of f(1000)-f(999) is greater than 12. Explain.

更新1:

without evaluating f(1000)-f(999)

更新2:

y not write it in like that way? 4(3^999) = 4 . 3 . 3^998 = 12 . 3^998 > 12

回答 (2)

六呎將軍

2009-11-07 6:36 am

✔ 最佳答案

f(1000) - f(999)

= 2(31000) - 2(3999)

= 2(3999)(3 - 1)

= 4(3999)

So it should be greater than 12 since 3999 > 1

2009-11-07 00:20:06 補充：
This is not evaluating cos the values are not given here.
Just factorization

2009-11-07 00:20:27 補充：
Also, 3^999 > 3

參考: Myself

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知識就是力量

2009-11-09 3:10 am

y not write it in like that way?

4(3^999)
= 4 . 3 . 3^998
= 12 . 3^998
> 12

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