Question

Plant growth The growth rate of a tree is predicted by G = In(a/m² +b/m +c) where m is the age of the tree, G is the growth, and a, b and c are constants. A scientist perform an experiment and measured the following data points mₑₓₚ = {2, 5, 10, 15, 20, 25, 30, 35, 40} months and Gₑₓₚ = {5.7,41., 3.3, 2.5, 2.1, 2.2, 1.7,1.6, 1.3} centimeters. Write a function PlantGrowth to calculate the coefficients a, b and c by using regression given experimental datasets mₑₓₚ and Gₑₓₚ and estimate the growth of the plant at a given month. Restriction: The function PlantGrowth must use polyfit. Hint: Linearize the dataset before performing a polynomial fit.

Answer 1

import numpy as np

def PlantGrowth(m_exp, G_exp, month):

a, b, c = np.polyfit(np.log(m_exp), G_exp, 2)

return np.log(a/month**2 + b/month + c)

The function PlantGrowth is designed to calculate the coefficients a, b, and c by performing a polynomial fit using the polyfit function from the NumPy library. The given experimental datasets for tree age (m_exp) and growth (G_exp) are used as input to the polynomial fit.

Since the growth rate equation is non-linear, a linearization technique is applied by taking the natural logarithm of the tree age (np.log(m_exp)) before performing the polynomial fit. The resulting coefficients represent the best-fit values for a, b, and c in the linearized equation.

Finally, the function uses the obtained coefficients to estimate the growth of the plant at a given month using the provided growth rate equation. The natural logarithm is applied to reverse the linearization and calculate the growth based on the original non-linear model.

This approach allows for a regression analysis that captures the underlying relationship between tree age and growth rate, providing a means to estimate growth for a given month based on the experimental data.