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Question 6 21 marks In, this question, where necessary, you. should. round answer's appropriately. (a) A student looking at global population gures remarks that between the years 1950 and 2010 the global population can be modelled by the equation 3003; = 23: 44 180 (1950 s t g 2010), where y is the global population in billions (109) at the start of year t, and t is the year. (i) Find the global population at the start of 1960 according to this model. [2] (ii) Explain the inequality [1950 S t S 2010) that follows the equation. [1] (iii) Using algebra, calculate the year in which the population passed 0 billion. [3] page 7 of 8 (iv) Write down the gradient of the straight line represented by the equation 300g = 23t 44 180 (1950 S t S 2010). \"lhat does this represent in the practical situation being modelled? [2] (v) Either using a suitable graph-sketching tool or by hand, sketch the graph of 300y = 231 44 130 (1950 g t g 2010), covering the time interval 1950 S t S 2010. [1] vi Ex lain wh the model cannot be extended to model accuratei the P y y population in 1800 or 2050. [2] (b) The student further observes that the global population between 1650 and 1927 can be modelled by the equation y = 1.246 x 10-4 x (1.005)t (1050 s t g 1927), where y is the global population in billions (109) at the start of year t, and t is the year. (i) Is this growth linear or exponential? Describe how growth rate differs between linear and exponential functions. [2] (ii) Calculate the population at the beginning of 1700 according to this model. [2] (iii) 1Write down the scale factor, and use this to nd the percentage increase in the population each year. [2] (iv) Use the method shown in Subsection 5.2 of Unit 13 to nd the year in which the population exceeds 1 billion. [4]