Which of the following is the most appropriate example of mathematical modelling?

Option 3 : Constructing a mathematical model for estimation of number of trees in a dense forest. 

A mathematical model is a mathematical relation that describes some real-life situation. The process of constructing mathematical models is known as mathematical modelling.

 In mathematical modelling, we describe a real-world problem as an equivalent mathematical problem. We then solve the mathematical problem and the solution is interpreted in the term of a real-world problem. After that, we check to determine if the answer is applicable to the real-world problem.

• A mathematical model is a translation of a real-world problem into a mathematical description. (Constructing a model for estimation of a number of trees in a dense forest).
• Performing experiments to understand and solve real-world problems may be risky and expensive. Also at times, it may be not feasible at all to perform experiments. Mathematical modelling is the only recourse in such situations it is very inexpensive if we can represent a real problem in terms of appropriate equations and solve them.

Hence, we conclude that the most appropriate example of mathematical modelling is constructing a mathematical model for the estimation of a number of trees in a dense forest.

While the other three examples do not represent a real-world situation.