Tasmania Jones' wheat field lies between two roads as shown in the diagram below. Main Road lies along the x-axis and Side Road lies along the curve with equation y = 3- e- y (km) a. b Side Road wheat field Main Road -a The y-axis intercept of the graph representing Side Road is b. Show that b=1. b. Find the exact value of a. x (km) a 1 mark 1 mark C. Since a is close to 1, Tasmania finds an approximation to the area of the wheat field by using rectangles of width 0.5 km, as shown on the following diagram. 2- 1.5- 0.5- -1 -0.5 -0.5- y (km) x (km) 0.5 2 i. Complete the table of values for y, where y = 3-ex-ex, giving values correct to two decimal places. x -0.5 0 0.5 y ii. Use the table to find Tasmania's approximation to the area of the wheat field, measured in square kilometres, correct to one decimal place. iii. Tasmania uses this approximation to the area to estimate the value of the wheat in his field at harvest time. He estimates that he will obtain w kg of wheat from each square kilometre of field. The current price paid to growers is $m per kg of wheat. Write a formula for his estimated value, SV, of the wheat in his field. d. Tasmania Jones decides to find another approximation to the area of the wheat field. He approximates the curve representing Side Road with a parabola which passes through the points (0, 1), (1, 0) and (-1, 0). He finds the area enclosed by the parabola and the x-axis as an approximation to the area of his wheat field. i. Find the equation of this parabola. ii. Find the area enclosed by the parabola and the x-axis, giving your answer correct to two decimal places. 1+2-3 marks e. Find the values of k, where k is a positive real number, for which the equation 3-ke* - e** = 0 has one or more solutions for x..