Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level31. Growth and Decay1. The relationship between x and y is given by the equation y = 1.5 – x .(a) Complete the table, giving y correct to 3 decimal places where necessary.x 0 1 2 3 4 5 6y 0.667 0.198(b) Draw the graph of y = 1.5 – x , allowing 2cm to represent 1 unit on the x axis and 2cm torepresent 0.1 on the y axis.(c) From your graph, estimate the following, showing clearly where your readings are taken.(i) the value of x when y = 0.7.(ii) the value of y when x = 3.5.2. The population of a country grows over a period of 7 years according to the equationP = P 0× 1.1 t where t is the time in years, P is the population after time t and P 0 is theinitial population.a) If = 10 million, complete the table below giving your values correct to 2 decimalplaces where necessary.P 05 1 2 --t 0 1 2 3 4 5 6 7P (million) 10 14.64 19.49b) Plot P against t. Allow 2cm to represent 1 year on the horizontal axis and 2cm torepresent 1 million on the vertical axis (Begin the vertical axis at 8 million).c) From your diagram estimate the population after years.d) How long will the population take to reach 15 million?3. The percentage of the nuclei remaining in a sample of radioactive material after time t isgiven by the formula P = 100 × a – t , where P is the percentage of the nuclei remainingafter t days and a is a constant.a) Copy and complete the table below for a = 3.t 0 0.5 1 1.5 2 2.5 3 3.5 4P 100 19.3 3.7b) Draw a graph showing P vertically and t horizontally. Use a scale of 4cm to represent 1day on the horizontal axis and 2cm to represent 10% on the vertical axis.c) From the graph, estimate the following, showing clearly where your readings are taken.(i) The half life of the material (ie when 50% of the nuclei remain) correct to the nearesthour.(ii) The percentage of the sample remaining after 2.25 days.(iii) The time at which three times as much remains as has decayed.