Question

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

x	y
1	0.04
2	0.16
3	0.64

answer attempt 1 out of 2
y =

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $y = ab^{x}$, where $a$ is the initial - value (when $x = 0$) and $b$ is the base.

Step2: Find the value of $a$

When $x = 0$, from the table $y=0.01$. Substituting $x = 0$ into $y = ab^{x}$, we get $y=a\times b^{0}=a$. So, $a = 0.01$.

Step3: Find the value of $b$

We know that $a = 0.01$, and when $x = 1$, $y = 0.04$. Substitute $a = 0.01$, $x = 1$, and $y = 0.04$ into $y = ab^{x}$:
$0.04=0.01\times b^{1}$.
Solve for $b$: $b=\frac{0.04}{0.01}=4$.

Answer:

$y = 0.01\times4^{x}$