- There are two questions in the Kim Iles Mathematical Challenge: a theoretical one and an applied one. Make sure that you answer both of them. - To be considered for the challenge, the solution must be submitted by June 1, 2023. Please upload your solution as a pdf file. - The award consists of a Certificate and $100.

Theoretical question

State the Basal Area Factor for Variable Plot Sampling (in Imperial units) for the following three angles: 90 degrees, 180 degrees, and 270 degrees. You can provide a full proof or briefly illustrate the geometry (10% reduction if the geometry is missing)

Practical question

A series of diameter measurements along the stem was executed on a set of Ponderosa Pines located on the east sides of the Cascades. The data, which contains the tree number (i.e., Tree), age at the time of the measurement (i.e., Age-in years), the total height of the tree (i.e., TotalHeight-in feet), the height of the measured diameter (i.e., DiamHeight-in feet), and the diameter at the specified height (i.e., Diameter-in inches), can be downloaded HERE. You are tasked to develop a taper equation with the following requirements:

· The model can have at most four (4) parameters (Note: values estimated from the data and used in the final form of the model are considered parameters).

· Achievement of a pseudo coefficient of determination of at least 95%

· Fulfillment of all modeling requirements, with tests included.

The assessment of the models will be executed using the following criteria, in descending order of importance:

1. The number of parameters used in the model

2. Fulfillment of modeling assumptions

3. The coefficient of pseudo-determination is >=0.95