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

$\dfrac{36}{9}=\dfrac{ab^2}{ab}$  

$4=b$  

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

$9=a(4)^1$

$\dfrac{9}{4}=a$

Putting $a=\dfrac{9}{4},b=4$ in (i), we get

$y=\dfrac{9}{4}(4)^x$

$y=9(4)^{x-1}$

The function notation with variable n is:

$f(n)=9(4)^{n-1}$

Therefore, the correct option is D.