Question

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

x	y
0	1
1	4
2	16
3	64

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 $x=0$

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

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

Substitute $a=1, x=1, y=4$:
$4 = 1 \times b^1$
So $b=4$.

Step4: Verify with other points

For $x=2$: $y=4^2=16$, which matches the table.
For $x=3$: $y=4^3=64$, which matches the table.

Answer:

$y = 4^x$