Question

equation of the exponential function represented by the table b

Explanation:

Step1: Identify base exponential form

The standard exponential function is $y = ab^x$, where $a$ is the initial value, $b$ is the growth factor.

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

When $x=0$, $y=0.2$. Substitute into $y=ab^x$:
$0.2 = ab^0$
Since $b^0=1$, $a=0.2$.

Step3: Calculate growth factor $b$

Use $x=1, y=0.6$ and $a=0.2$:
$0.6 = 0.2b^1$
Solve for $b$: $b = \frac{0.6}{0.2} = 3$
Verify with other points: For $x=2$, $y=0.2(3)^2=0.2\times9=1.8$, which matches the table. For $x=3$, $y=0.2(3)^3=0.2\times27=5.4$, which also matches.

Answer:

$y = 0.2(3)^x$