Question

find the equation of the exponential function.

$x$	$f(x)$
1	$1\cdot2$
2	$1\cdot(2)^2$
3	$1\cdot(2)^3$

$\boldsymbol{x}$ $\boldsymbol{+}$ $\boldsymbol{-}$ $\boldsymbol{\ast}$ $\boldsymbol{\frac{\square}{\square}}$ $\boldsymbol{\div}$
$\boldsymbol{\pm}$ $\boldsymbol{a^b}$ $\boldsymbol{a^2}$ $\boldsymbol{\square^3}$ $\boldsymbol{e^x}$ $\boldsymbol{\square_0}$
$f(x)=$

Explanation:

Step1: Recall exponential form

The general exponential function is $f(x) = a \cdot b^x$, where $a$ is the initial value, $b$ is the base.

Step2: Find $a$ using $x=0$

When $x=0$, $f(0)=1$. Substitute into the formula:
$1 = a \cdot b^0$
Since $b^0=1$, $a=1$.

Step3: Identify base $b$

For $x=1$, $f(1)=1 \cdot 2$; $x=2$, $f(2)=1 \cdot 2^2$; $x=3$, $f(3)=1 \cdot 2^3$. The base $b=2$.

Step4: Write the final function

Substitute $a=1$ and $b=2$ into $f(x)=a \cdot b^x$.

Answer:

$f(x)=2^x$