question\nfind the equation of the exponential function represented by the table below:\n\nanswer\ny =

Explanation:

Step1: Recall exponential form

The general exponential function is $y = ab^x$, where $a$ is the y-intercept, $b>0, b\neq1$.

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: Find $b$ using another point

Use $x=1, y=0.04$. Substitute $a=0.02$ into $y=ab^x$: $0.04 = 0.02b^1$ Solve for $b$: $b = \frac{0.04}{0.02}=2$

Step4: Write the final equation

Substitute $a=0.02$ and $b=2$ into $y=ab^x$.

Answer:

$y = 0.02(2)^x$