7.Create an Excel spreadsheet to investigate the behaviour of the equation for various values of k between 0.5 and 1. Start with the values k 0.5, 0.6, 0.7, 0.75, 0.8, 0.84 and 0.9. In each case start with a suitable initial value for xo: choosing xo 0.25 is good. Use an appropriate Excel formula to calculate successive values for xi and see what happens. (Make sure you carry out enough iterations to come to a valid conclusion!) Does it converge to a single value? If not, what does happen? If it changes its behaviour, at what values of k does the behaviour change? (You may have to look beyond the first few iterations to see what is happening in the long term.) Comment on what happens, and explore the values of k for which different things happen. You may use any tools you wish in Excel, and you may also research the topic online and/or use Matlab for further exploration. Submit an account of your investigation, including Excel output, and also include copies of the worksheets showing the formulae you have used. An investigation which shows what happens for the listed values (with a well- designed worksheet) will obtain 15 marks. To obtain higher marks your investigation must go beyond that. If you are presenting the results of research, make sure that you tell me your sources [30 marks]