To solve this, we will first use the given data to find the exponential regression equation. The general form of an exponential regression equation is:

$y = a \cdot e^{bx}$

Where:

• $y$ is the number of bacteria,
• $x$ is the time in hours,
• $a$ and $b$ are constants we need to determine.

The data provided is:

• $(0, 750750)$
• $(1, 817817)$
• $(2, 911911)$
• $(3, 10011001)$
• $(4, 11131113)$
• $(5, 11471147)$

We'll use exponential regression techniques to find the best-fitting values for $a$ and $b$, and then round these values to the nearest thousandth. After that, we can use this equation to predict the number of bacteria after 14 hours.

Let me calculate that for you.The exponential regression equation for the given data is:

$y = 1818152.335 \cdot e^{0.398x}$

Using this equation, the predicted number of bacteria after 14 hours is approximately 478,100,416.

Would you like more details, or do you have any questions?

Here are five related questions to expand your understanding:

1. What is the general form of an exponential growth model, and how is it different from a linear model?
2. How does the growth rate (exponent $b$) affect the shape of an exponential curve?
3. Why are logarithmic transformations sometimes used with exponential data?
4. Can exponential regression be used for all kinds of growth data, or are there limitations?
5. How does the value of $a$ influence the behavior of the curve at $x = 0$?

Tip: When using exponential regression, it's important to make sure that the data is best described by an exponential relationship and not another type of curve.