Question

You are given monthly data on the total population of sandhill cranes in a small portionof the Florida Everglades over a period of one year. You want a continuous model forthe crane population which agrees with the observed monthly population and is also twicedifferentiable at any time strictly between zero and one year.

Answer 1

Complete Question:

You are given monthly data on the total population of sandhill cranes in a small portionof the Florida Everglades over a period of one year. You want a continuous model forthe crane population which agrees with the observed monthly population and is also twice differentiable at any time strictly between zero and one year.

Which of these modelling tools match this modelling situation: (i) Markov chain (ii) Linear Interpolation (iii) Second order differential equation (iv) First order separable differential equation (v) cubic spline interpolation (vi) Line of regression (vii) R² (viii) First order recurrence relation.

Answer:

Second order differential equation

Explanation:

A second order differential equation is an equation involving the unknown function y, its derivatives y' and y'', and the variable x.

Since it is said in the modelling situation that the population is twice differentiable at any time strictly between zero and one year. This means that the situation can be modeled using a second order differential equation
`(d^(2)P )/(dt^(2) )` for 0 < t < 1

Where P is the total population of sandhill cranes and

t = the period