Question

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

x	y
0	4
1	12
2	36
3	108

answer attempt 2 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, $x$ is the input, and $y$ is the output.

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

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

Step3: Solve for growth factor $b$

Use $x=1$, $y=12$ and $a=4$:
$12 = 4b^1$
Divide both sides by 4: $b = \frac{12}{4} = 3$
Verify with $x=2$: $y=4\times3^2=4\times9=36$, which matches the table.

Step4: Write final equation

Substitute $a=4$ and $b=3$ into $y=ab^x$.

Answer:

$y = 4(3)^x$