nlsq.core.functions.exponential_growth

nlsq.core.functions.exponential_growth(x, a, b, c)[source]

Exponential growth: y = a * exp(b*x) + c

Common for population growth, compound interest, bacterial growth.

Parameters:

  • x (array_like) – Independent variable (time, distance, etc.)

  • a (float) – Initial amplitude

  • b (float) – Growth rate (positive, units: 1/x)

  • c (float) – Offset (baseline)

Returns:

y – Dependent variable

Return type:

array_like

Notes

  • Doubling time: t_double = ln(2) / b

  • At x=0: y = a + c

  • As x→∞: y → ∞ (unbounded growth)

Examples

>>> from nlsq import curve_fit
>>> from nlsq.core.functions import exponential_growth
>>> import numpy as np
>>>
>>> # Bacterial growth with doubling time = ln(2)/0.3 ≈ 2.3
>>> x = np.linspace(0, 5, 50)
>>> y = 10 * np.exp(0.3 * x) + np.random.normal(0, 1, 50)
>>> popt, pcov = curve_fit(exponential_growth, x, y, p0='auto')
>>> print(f"Doubling time: {np.log(2)/popt[1]:.2f}")