Question

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

answer
y =

Explanation:

Step1: Recall exponential form

The general form of an exponential function is $y = ab^x$, where $a$ is the initial value, $b$ is the growth factor, $x$ is the input, and $y$ is the output.

Step2: Find $a$ using $x=0$

When $x=0$, $y=4$. Substitute into the formula:
$4 = ab^0$
Since $b^0 = 1$, we get $a = 4$.

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

Now use $x=1$, $y=12$, and $a=4$:
$12 = 4b^1$
Solve for $b$: $b = \frac{12}{4} = 3$

Step4: Verify $b$ with other points

Check $x=2$: $y = 4\times3^2 = 4\times9 = 36$, which matches the table.
Check $x=3$: $y = 4\times3^3 = 4\times27 = 108$, which matches the table.

Answer:

$y = 4(3)^x$