Question

What function represents the pattern shown in the table?

Answer 1

Given:

The table of values of an exponential function.

To find:

The function for the given table of values.

Solution:

The general exponential function is:

`y=ab^x` ...(i)

Where, a is the initial value and b is growth factor.

From the given table it is clear that the function passes through the points (1,9) and (2,36). It means the function must be true for these two points.

`9=ab^1` ...(ii)

`36=ab^2` ...(iii)

On dividing (iii) by (ii), we get

`(36)/(9)=(ab^2)/(ab)`

`4=b`

Putting
`b=4` in (ii), we get

`9=a(4)^1`

`(9)/(4)=a`

Putting
`a=(9)/(4),b=4` in (i), we get

`y=(9)/(4)(4)^x`

`y=9(4)^(x-1)`

The function notation with variable n is:

`f(n)=9(4)^(n-1)`

Therefore, the correct option is D.