Question

find the equation of the exponential function represented by the table below:

x	y
1	2
2	4
3	8

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $y = ab^{x}$, where $a$ is the initial - value (when $x = 0$) and $b$ is the base.

Step2: Find the value of $a$

When $x = 0$, from the table $y=1$. Substituting $x = 0$ and $y = 1$ into $y = ab^{x}$, we get $y=a\times b^{0}=a$. Since $b^{0}=1$ for $b
eq0$, then $a = 1$.

Step3: Find the value of $b$

We know $a = 1$, so the function is $y=b^{x}$. Using the point $(1,2)$ (we can also use other non - zero $x$ points), substitute $x = 1$ and $y = 2$ into $y=b^{x}$. We have $2=b^{1}$, so $b = 2$.

Answer:

$y = 2^{x}$