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Math Expert V
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The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of  [#permalink]

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The function f(x) is defined by $$f(x)=100−2^x$$. If f(x)=6, then which of the following is true about the value of x?

A. 0≤x≤4

B. 4<x≤8

C. 8<x≤16

D. 16<x≤32

E. 32<x≤64

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Joined: 12 Sep 2015
Posts: 4003
Re: The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of  [#permalink]

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Bunuel wrote:
The function f(x) is defined by $$f(x)=100−2^x$$. If f(x)=6, then which of the following is true about the value of x?

A. 0≤x≤4

B. 4<x≤8

C. 8<x≤16

D. 16<x≤32

E. 32<x≤64

If f(x) = 6, then 100 - 2^x = 6
Rearrange to get: 2^x = 94

Observe:
2^6 = 64
2^7 = 128

Since 94 is BETWEEN 64 and 128, we can conclude that x is BETWEEN 6 and 7

Only answer choice B meets the criteria that x is BETWEEN 6 and 7

Cheers,
Brent
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Re: The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of  [#permalink]

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Bunuel wrote:
The function f(x) is defined by $$f(x)=100−2^x$$. If f(x)=6, then which of the following is true about the value of x?

A. 0≤x≤4

B. 4<x≤8

C. 8<x≤16

D. 16<x≤32

E. 32<x≤64

We are given that f(x) = 100 - 2^x and that f(x) = 6. Thus:

6 = 100 - 2^x

2^x = 94

We are looking for a number such that 2 raised to that number is equal to 94. We know that 2^6 = 64 and 2^7 = 128. Therefore, even though we can’t determine the exact value of x (unless we have a calculator), we know that 6 < x < 7. Since 6 < x < 7, the correct answer choice is B: 4 < x ≤ 8.

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Re: The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of  [#permalink]

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Bunuel wrote:
The function f(x) is defined by $$f(x)=100−2^x$$. If f(x)=6, then which of the following is true about the value of x?

A. 0≤x≤4

B. 4<x≤8

C. 8<x≤16

D. 16<x≤32

E. 32<x≤64

f(x) = 6 = 100 - 2^x
2^x = 94
2^6 = 64
and 2^7 = 128
6<x<7

Only B. 4<x≤8 satisfies the criteria

IMO B
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E-mail : kinshook.chaturvedi@gmail.com Re: The function f(x) is defined by f(x)=100−2^x. If f(x)=6, then which of   [#permalink] 08 Oct 2019, 02:14
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