SUSTAINABLE FALLING OF TREES

A community, with Otomi roots, in the municipality of Villa del Carb$$n$,$ State of Mexico, is dedicated to the cultivation and use of timber resources in the region $($these are not ornamental trees, they are coniferous$-$oyamel forests$).$Despite the technical advice available to them, offered by agricultural engineers from Chapingo, there is an important question to which they do not have a concrete answer, namely:

THE CENTRAL QUESTION OF THE PROBLEM: What is the most convenient time for felling trees?

The following table shows estimated data that establishes the relationship of the total volume of wood $($m$^3/$hectare$)$ versus planting time in the rural area of $$the State of Mexico, Villa del Carb$$n$.$

Towards the mathematical solution of the problem situation.

$7.$ Graph the points in Table $1.$ Agronomists frequently use an adjustment function of the type:

V$($t$)=$ e$^(($a$+$b$)/$t$)$

Fit the data in Table $1$ to a function of this type.

$8.$ Fit the data in Table $1$ to a polynomial type function. Is another type of functional fit possible?

$9.$ Prepare a mathematical discussion regarding the first time period: $[0,1].$ Your explanation must make a contrast that explains the difference in this time interval between the functional models of the proposals in points $7$ and $8.$