Question

What is the exponential function modeled by the following table?

Answer 1

Answer:

$f(x)=9^{x-1}$

Step-by-step explanation:

The general form of the exponential function is,

$y=ab^x$

The points on the graph will be,

$(2,9),(3,27),(4,81)$

Putting the points in the function,

$9=ab^2$  -----------------------------------1

$27=ab^3$  ---------------------------------2

Dividing equation 2 by equation 1,

$\Rightarrow \dfrac{27}{3}=\dfrac{ab^3}{ab^2}$

$\Rightarrow 9=\dfrac{b^3}{b^2}$

$\Rightarrow b=9$

Putting the value of b in equation 1,

$\Rightarrow a(9)^2=9$

$\Rightarrow a=\dfrac{9}{9^2}$

$\Rightarrow a=\dfrac{1}{9}$

Putting all the values,

$\Rightarrow y=\dfrac{1}{9}\cdot 9^x$

$\Rightarrow y=9^{x-1}$

Answer 2

3^2 = 9
3^3 = 27
4^3 = 81 
so f(x) =  3^x