Question

find the equation of the exponential function.

$x$

$f(x)$

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0

1

1

$1\cdot2$

2

$1\cdot(2)^2$

3

$1\cdot(2)^3$

$f(x)=a\cdot b^x$

$1=a\cdot b^0$
$b^0=1$
$a=1$

$f(x)=$

Explanation:

Step1: Identify base $b$ from table

From $x=1$, $f(1)=1\cdot2$, so $b=2$.

Step2: Confirm $a$ value

We already have $a=1$ from $x=0$.

Step3: Substitute into exponential form

Use $f(x)=a\cdot b^x$ with $a=1, b=2$.
<Expression>
$f(x)=1\cdot 2^x$
</Expression>

Answer:

$f(x)=2^x$