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2 votes
2 votes
(1, 4), (2, 8), (3, 16), (4, 32)

write a function to represent the data and show your work​

User Thev
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1 Answer

8 votes
8 votes

Answer:

f(x)=4(2)^x-1, or f(1)=4,f(x)=f(x-1)(2)

Explanation:

The first equation above is the Explicit Geometric Formula, while the equation on the right is the Recursive Geometric Formula. This is how you find both.

Explicit Geometric Formula:

The formula for this is f(x)=a(r)^x-1, a being the first term, and r being the common ratio.

A, our starting term, or first term, is x = 1, and the term is 4, since that is the corresponding y to x = 1.

Our common ratio is 2, because as x increases by 1, y doubles.

Recursive Geometric Formula:

The formula for this is f(1)=a,f(x)=f(x-1)(r), a being the first term, and r being the common ratio.

As said above, A is 4, and r is 2.

Plug it in and you get f(1)=4,f(x)=f(x-1)(2)

User Iya
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