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 =

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: Find $a$ using $x=0$

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

Step3: Find $b$ using $x=1$

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

Step4: Write final equation

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

Answer:

$y=2^x$