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What function does this table make

What function does this table make-example-1
User Jim Cote
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1 Answer

3 votes

Answer:

f(n) = 3^(n -1)

Explanation:

You want a function that describes the relation shown in the table.

Analysis

The values under Steps are sequential, which makes determining the function a lot easier.

The values listed under Black Triangles don't have a common difference, but they do have a common ratio:

r = 3/1 = 9/3 = 27/9 = 3

Exponential function

For this function, we'll use 'n' as the independent variable (the number of steps), and we'll call the function 'f'.

For common ratio r and a pair of table values (n, f(n)) = (a, b), the exponential function can be written as ...

f(n) = b·r^(n -a)

With r=3 and (a, b) = (1, 1), this becomes ...

f(n) = 1·3^(n -1)

The multiplier 1 isn't really needed, so we can use ...

f(n) = 3^(n -1)

User Shadeglare
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