Question

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

x	y
1	0.08
2	0.32
3	1.28

answer
y =

Explanation:

Step1: Recall exponential form

The general exponential function is $y = ab^x$, where $a$ is the y-intercept (value when $x=0$).

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

When $x=0$, $y=0.02$. Substitute into $y=ab^x$:
$0.02 = ab^0$
Since $b^0=1$, $a=0.02$.

Step3: Solve for growth factor $b$

Use $x=1, y=0.08$ and $a=0.02$:
$0.08 = 0.02b^1$
$b = \frac{0.08}{0.02} = 4$

Step4: Verify $b$ with other points

Check $x=2$: $y=0.02(4)^2=0.02(16)=0.32$, which matches.
Check $x=3$: $y=0.02(4)^3=0.02(64)=1.28$, which matches.

Answer:

$y = 0.02(4)^x$