Question 1 (14 marks) Griffin house decides to try out two new instruments. The first is called a HeebiephonLE; which is very difficult to play. The Sonorousness (richness of the sdund measured in dB} of the Heebiephone is given by the formula: H: [0; 4] ) R, Ha) = t3 13t + 12 (where t is time in minutes) a. Find the average rate of change between t = 1 and t = 2. , [1 mark) I). Find the instantaneous rate of change at t : 3. [1 mark] c. Fins! the real values of p for which the equation H(t) = t3 13t + 12 = p, (2 marks) where t e [0, 4] has exactly one solution. The second instrument is a Pixiephone. The Sonorousness of the Pixiephone is given by the formula: P: [0, 4] -> R, P(t) = - (t2 - 9) ($2 - 1) where t is time in minutes The Griffin music leader, Tammi, has heard that audiences are influenced by the Sonorousness of the opening note. d. Find the initial Sonorousness for each instrument and state which instrument is greater (2 marks)The other Griffin music leader, Amanda, has determined that changes in sound are important and that the turning points of the functions might be an important factor. ei. Find the location and nature of any turning points for each instrument. (2 marks) ii. State which instrument has the highest Sonorousness over the given domair ( 1 mark) The Griffin House Music captains decide to adjust the instruments to increase the Sonorousness of both instruments. f. Find the rule of the image of the graph of H(t) = to - 13t + 12 under the following (2 marks) sequence of transformations: Dilation by a factor of 5 from the x-axis Reflection in the x-axis Translation of 10 units in the positive direction of the y-axisg. Find the rule of the image of the graph P(t) = - (t2 - 9) (t? - 1) under the transformations (2 marks) dilation by a factor of = from the x-axis reflection in the x-axis translation 10 unit in the negative direction of the x-axis. h. State which instrument has the highest Sonorousness under these transformations (1 mark)