Let's solve the given problem step by step.

We need to find an exponential function in the form:

$y = ab^x$

Step 1: Use the first point $(0, 17)$

When $x = 0$, $y = 17$. Substituting into $y = ab^x$:

$17 = ab^0$

Since $b^0 = 1$, this simplifies to:

$a = 17$

So, the equation becomes:

$y = 17b^x$

Step 2: Use the second point $(3, 8704)$

Substitute $x = 3$ and $y = 8704$ into $y = 17b^x$:

$8704 = 17b^3$

Solve for $b^3$ by dividing both sides by 17:

$b^3 = \frac{8704}{17} = 512$

Now, take the cube root of both sides to find $b$:

$b = \sqrt[3]{512} = 8$

Step 3: Write the final equation

Now substitute $a = 17$ and $b = 8$ into the equation:

$y = 17 \cdot 8^x$

This is the required exponential function.

Would you like further explanation or clarification? Let me know!

Here are some related questions to extend your understanding:

1. How would the process change if one of the points was $(1, 50)$ instead of $(0, 17)$?
2. What is the significance of the value of $a$ in the function $y = ab^x$?
3. How can you determine if two points define a valid exponential function?
4. What happens if $b < 1$? How would the graph of the function look?
5. How can you verify your function by substituting other values of $x$?

Tip: Always start solving exponential functions by finding $a$ using the point where $x = 0$, as it simplifies the equation.