Question

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

$x$	$y$
1	15
2	45
3	135

answer
$y =$

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 $x=0$, $y=5$. Substitute into the formula:
$5 = ab^0$
Since $b^0=1$, we get $a=5$.

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

Substitute $x=1$, $y=15$, $a=5$ into the formula:
$15 = 5b^1$
Solve for $b$: $b = \frac{15}{5}=3$

Step4: Write final equation

Substitute $a=5$ and $b=3$ into $y=ab^x$.

Answer:

$y=5(3)^x$