Question

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

x	y
1	2
2	4
3	8

answer
attempt 1 out of 2
y = \boxed{}

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 $b^0=1$, we get $a=1$.

Step3: Find $b$ using another point

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

Step4: Verify with other points

Check $x=2$: $y=1 \times 2^2 = 4$, which matches the table.
Check $x=3$: $y=1 \times 2^3 = 8$, which matches the table.

Answer:

$y=2^x$