Question

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

x	y
0	5
1	15
2	45
3	135

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $y = ab^{x}$, where $a$ is the initial value and $b$ is the base.

Step2: Find the value of $a$

When $x = 0$, $y=ab^{0}=a$. From the table, when $x = 0$, $y = 5$, so $a = 5$.

Step3: Find the value of $b$

Substitute $a = 5$, $x = 1$, and $y = 15$ into $y=ab^{x}$. We get $15=5b^{1}$. Solving for $b$ gives $b=\frac{15}{5}=3$.

Answer:

$y = 5\times3^{x}$