numpy as np import pandas as pd from scipy.optimize import curve_fit

Data points

x = np.array([1, 2, 3, 4, 5, 6]) y = np.array([1173, 2093, 3380, 5793, 9828, 16673])

Define the exponential function

def exponential_func(x, a, b): return a * (b ** x)

Fit the curve

params, _ = curve_fit(exponential_func, x, y, p0=(1, 1))

Extracting the parameters a and b

a, b = params a, bThe exponential equation that best fits the data is:

$y = 701.75 \cdot (1.6955)^x$

Where:

• $a = 701.75$
• $b = 1.6955$

Would you like a detailed explanation of the regression process or the steps involved in deriving this equation?

Here are five related questions you might find interesting:

1. How can I interpret the parameters $a$ and $b$ in this context?
2. What are the steps to compute the goodness-of-fit for this model?
3. Can this equation be used for extrapolation beyond the given data range?
4. How does an exponential fit differ from a polynomial fit for this data?
5. What is the meaning of regression in general, and why is it important in data analysis?

Tip: Always assess the goodness-of-fit using metrics like R² or residuals to ensure the model is appropriate for the data.