Question

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

x	y
0	1
1	2
2	4
3	8

answer attempt 1 out of 2
$y = \square$

Explanation:

Step1: Recall exponential form

The general exponential function is $y = ab^x$, where $a$ is the initial value, $b$ is the growth factor.

Step2: Solve for $a$ using $x=0$

When $x=0$, $y=1$. Substitute into the formula:
$1 = ab^0$
Since $b^0=1$, we get $a=1$.

Step3: Solve for $b$ using $x=1$

Now use $x=1$, $y=2$ and $a=1$:
$2 = 1 \times b^1$
This simplifies to $b=2$.

Step4: Write the final equation

Substitute $a=1$ and $b=2$ into $y=ab^x$.

Answer:

$y=2^x$