To find the exponential regression equation for the given data set, we assume an equation of the form:

$y = ab^x$

where:

• $y$ is the number of bacteria,
• $x$ is the time in hours,
• $a$ is the initial quantity of bacteria at $x = 0$,
• $b$ is the growth factor per unit of time (in hours).

Given Data Points:

Hours (x)	Bacteria (y)
0	1221
1	1332
2	1437
3	1576
4	1698

We will use exponential regression to find the best-fit values for $a$ and $b$. Let me calculate that for you.

The exponential regression equation for the given data set is:

$y = 1223.15 \times (1.09)^x$

Using this equation, the estimated number of bacteria after 9 hours is approximately:

$2573 \text{ bacteria}$

Would you like further clarification or details about this solution?

Here are some related questions:

1. How would the growth factor change if the rate of bacteria growth increases?
2. Can exponential growth continue indefinitely? Why or why not?
3. What are some real-world scenarios where exponential regression is used?
4. How does exponential growth differ from linear growth?
5. What is the significance of the base $b$ in the exponential equation?

Tip: In exponential growth, the quantity increases by a fixed percentage (or factor) per time unit, unlike in linear growth where the increase is by a fixed amount.