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 attempt 1 out of 2

y =
submit answer

Explanation:

Step1: Recall exponential form

The general exponential function is $y = ab^x$, where $a$ is the y-intercept, $b$ is the growth factor.

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

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

Step3: Calculate growth factor $b$

Use $x=1, y=0.08$ and $a=0.02$:
$0.08 = 0.02b^1$
Solve for $b$: $b = \frac{0.08}{0.02} = 4$
Verify with $x=2$: $y=0.02(4)^2=0.02(16)=0.32$, which matches the table.

Step4: Write final equation

Substitute $a=0.02$ and $b=4$ into $y=ab^x$.

Answer:

$y = 0.02(4)^x$