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import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

# Example data
# Replace x_data and y_data with your actual dataset
x_data = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
y_data = np.array([2.3, 3.1, 4.5, 6.2, 8.0, 10.1, 12.5, 15.3, 18.2, 22.1])

# Define the model function: y = a * x^b
def power_law(x, a, b):
    return a * np.power(x, b)

# Use curve_fit to fit the model to the data
params, covariance = curve_fit(power_law, x_data, y_data)

# Get the fitted parameters a and b
a, b = params
print(f"Fitted parameters: a = {a}, b = {b}")

# Generate values using the fitted model for plotting
x_fit = np.linspace(min(x_data), max(x_data), 100)
y_fit = power_law(x_fit, a, b)

# Plot the original data and the fitted curve
plt.scatter(x_data, y_data, label="Data", color="red")
plt.plot(x_fit, y_fit, label=f"Fitted Curve: y = {a:.2f} * x^{b:.2f}", color="blue")
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()