Matrices and function - Coursework Example

0.0072 = 0.9928 are alive at the end of the year. Some of this number will have reached the age of 15 during the 1 year and become adults. We shall assume that15 of the surviving juveniles become adults. So the proportion of juveniles still alive and still juveniles at 14 the end of the year is . (b) The network model above can be written as a matrix equation of the form where M is a 2 x 2 matrix. Write down the matrix M (c) (i) Edit the matrix M, and the vector whose entries are the initial subpopulation sizes J0 and A0, in a copy of a worksheet so that the worksheet shows the predicted changes in population size for the country considered in this question.

Set N = 50, so that the worksheet covers 50 years. Here we have: For n=0, For n= 2, As the value is influenced by the previous value the table has the accurate calculation: Table below shows the juvenile population, Adult population and total population, while the first column shows the increase in the years startind from 2007 and ending at 2057. n Jn An Tn 0 8.3 30.1 38.4 1 8.82254 30.09562 38.91816 2 9.306561 30.12591 39.43247 3 9.756194 30.18769 39.94388 4 10.17515 30.2781 40.45324 5 10.56675 30.39457 40.96132 6 10.93398 30.53483 41.

46882 7 11.27954 30.69682 41.97636 8 11.60582 30.87871 42.48453 9 11.91499 31.07884 42.99384 10 12.209 31.29576 43.50476 11 12.48958 31.52816 44.01774 12 12.7583 31.77485 44.53315 13 13.01658 32.03479 45.05137 14 13.26567 32.30705 45.57272 15 13.50671 32.59079 46.0975 16 13.74073 32.88526 46.626 17 13.96865 33.18981 47.15846 18 14.19129 33.50384 47.69513 19 14.40939 33.82683 48.23623 20 14.62363 34.15832 48.78195 21 14.83461 34.49789 49.3325 22 15.04287 34.84518 49.88805 23 15.2489 35.19987 50.

44877 24 15.45315 35.56167 51.01482 25 15.65601 35.93033 51.58634 26 15.85784 36.30564 52.16348 27 16.05896 36.68741 52.74637 28 16.25968 37.07546 53.33514 29 16.46026 37.46966 53.92992 30 16.66093 37.86989 54.53083 31 16.86193 38.27604 55.13797 32 17.06344 38.68802 55.75146 33 17.26566 39.10576 56.37142 34 17.46873 39.5292 56.99793 35 17.67283 39.95829 57.63112 36 17.87807 40.393 58.27108 37 18.0846 40.8333 58.9179 38 18.29252 41.27917 59.57169 39 18.50195 41.7306 60.23254 40 18.71297 42.18758 60.

90056 41 18.9257 42.65013 61.57582 42 19.14019 43.11825 62.25844 43 19.35655 43.59195 62.9485 44 19.57484 44.07126 63.6461 45 19.79512 44.55621 64.35133 46 20.01747 45.04681 65.06428 47 20.24195 45.54311 65.78506 48 20.46861 46.04513 66.51374 49 20.69751 46.55292 67.25044 50 20.92871 47.06652 67.99523 51 21.16224 47.58598 68.74822 (ii) What behaviour does the model predict for the total population size over 50 years? Find the sizes of the total population predicted by the model for the years 2032 and 2057, giving your answers to the nearest thousand.

The population of the juveniles and the adults in total is increasing by the ration of 1.013 and the population is increasing in the geometric manner. The size of the population in the year 2032 will be at 51.58634 million which is approximately 1.343 times the total population in the year 2007. In the 2057, the total population of juveniles and adults will be 67. 99523 million, which is 1.77 times the population in the year 2007. (iii) What does the model predict for the ratio of successive total populations over the 50 years?

Your answer should include both a description of behaviour and numerical information. Years Tn Ratio Tn/Tn-1 2007