To determine the exponential regression equation and the number of bacteria after 9 hours, I will calculate the equation of the form:

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

Where:

• $a$ and $b$ are the constants to be determined through regression analysis.
• $x$ represents the time (in hours).
• $y$ represents the number of bacteria.

Let me calculate this for you.import numpy as np from scipy.optimize import curve_fit import pandas as pd

Data points

x = np.array([0, 1, 2, 3, 4]) # Hours y = np.array([853853, 918918, 10151015, 10581058, 11781178]) # Bacteria count

Exponential function

def exponential_func(x, a, b): return a * np.exp(b * x)

Curve fitting

params, _ = curve_fit(exponential_func, x, y) a, b = params

Predict bacteria count after 9 hours

hours = 9 predicted_bacteria = exponential_func(hours, a, b)

Round coefficients and prediction

a_rounded = round(a, 3) b_rounded = round(b, 3) predicted_bacteria_rounded = round(predicted_bacteria)

a_rounded, b_rounded, predicted_bacteria_rounded(2841105.541, 0.385, 90841295)(2841105.541, 0.385, 90841295)successThe exponential regression equation is:

$y = 2841105.541 \cdot e^{0.385x}$

Using this equation, the number of bacteria present after 9 hours is approximately 90,841,295.

Do you want a detailed explanation or have further questions?
Here are 5 related questions you might explore:

1. How is exponential regression applied in other scientific contexts?
2. What are the implications of rapid bacterial growth in real-world scenarios?
3. Could we use a different type of regression for this data, such as polynomial regression?
4. What happens if growth slows down or levels off over time?
5. How does rounding coefficients impact prediction accuracy?

Tip: Always plot your data and the regression line to visually verify the fit!