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Given the sequence 2, 4, 8, , 16,........, where x = 0, 1, 2, 3, .......what is the function rule? f(x) = 2x + 2 f(x) = 2(2)x f(x) = (2x) f(x) = 2

User Caheem
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1 Answer

4 votes

Option C:
f(x)=2^x is the function rule.

Step-by-step explanation:

The sequence is
2,4,8,16, \dots \dots

Let us find the common difference of this sequence.

Common ratio =
(4)/(2) =2

Hence,
r=2

Thus, the given sequence is a geometric progression.

To determine the function rule, let us substitute the values in the general formula of GP which is given by


f(x)=ar^(x-1) where
a=2, r=2

Substituting we get,


f(x)=2(2)^(x-1)

Simplifying, we get,


f(x)=2*2^x*2^{-1

Adding the powers, we get,


f(x)=2^(1+x-1)

Simplifying, we get,


f(x)=2^x

Hence, the function rule is
f(x)=2^x

Thus, Option C is the correct answer.

User Krupal Tharwala
by
8.2k points

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