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Harrizon [31]
2 years ago
14

Given that a geometric sequence can be expressed as a non-linear function in the form f(x) = abx, write a non-linear function to

describe the sequence {3, 6, 12, 24, 48, 96, ...}.
Mathematics
2 answers:
Svetlanka [38]2 years ago
4 0

Answer:

f(x)=\dfrac{3}{2}(2)^x

Step-by-step explanation:

The given sequence is

{3, 6, 12, 24, 48, 96, ...}

It means f(x)=3, 6, 12, 24, 48, 96, ... for x=1,2,3,4,5,6,.. respectively.

We need to find non-linear function in the form  

f(x)=ab^x       ...(1)

We know that f(x)=3 for x=1.

3=ab^1          ....(i)

We know that f(x)=6 for x=2.

6=ab^2          ....(ii)

Divide equation (ii) by (i).

\dfrac{6}{3}=\dfrac{ab^2}{ab}

2=b

Substitute b=2 in equation (1).

3=a(2)^1

\dfrac{3}{2}=a

Substitute a=\dfrac{3}{2} and b=2 in (1).

f(x)=\dfrac{3}{2}(2)^x

Therefore, the required function is f(x)=\dfrac{3}{2}(2)^x.

guajiro [1.7K]2 years ago
3 0

f(x) = 3 \times  {2}^{x}

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