To complete successfully this homework, you must read the Chapters 3 Markoy Chain po 122-127. and Chapter 5 Continuous Models in our textbook A Course in Math- ematical Modeling pg.258-260 and 283-, and Chapter 3 Linear Programming pg. 39 from the reference textbook Mathematical Modeling: A Comprehensive Introduction. Use one of the software tools: Excel, SPSS, Mathematica, or MATLAB to answer the fol lowing items, and print out your results directly from the software, 1. Describe the fundamentals of a Markov Chain Model and provide two examples of Markov chain. 2. Showing that a model is valid can be difficult. Often it is much easier to show that a model is invalid. Consider the following model that has been proposed to describe the growth of redwoods (Sequoia sempervirens). Redwoods frequently live 1,000 years or more. The model used classifies redwoods into three age stages: 0 to 200 years (young), 200 to 800 (mature), and older than 800 (old). A current census in a particular stand finds that currently there are 1,696 young redwoods, 485 mature redwoods, and 82 old redwoods. The transition between stages over a 50-year period is given by the matrix / 12 26 6 T= 0.30.920 0 0.18 0.67 Trace this stand of trees through five time steps (five 50-year periods for a total of 250 years) and explain how we know that this model cannot possibly be valid