Show ALL WORK and ANSWERS on the exam A national financial s…

Show ALL WORK and ANSWERS on the exam A national financial study tracks the growth of average household credit card debt over several decades.Let: y represents the average credit card debt in dollars. x represents the number of years after 1990, so: x = 0,    corresponds to 1990, x = 4,    corresponds to 1994, x = 10,  corresponds to 2000, x = 13,  corresponds to 2003, and so on. From one of the more detailed charts, the researcher relies on two trustworthy data points (all other data were incomplete or estimated and cannot be used): In 1990, the average household credit card debt was $4,275. In 2008, the average household credit card debt had increased to $11,940. This gives her the two ordered pairs:  (0,4275) and (18,11940) Your Tasks Use the two ordered pairs to create a linear equation that models average credit card debt as a function of the year x .Round the slope to the nearest tenth. Use your model to estimate the average credit card debt in 2003.Round your answer to the nearest dollar.    

Show ALL WORK and ANSWERS on the exam A theme park is testin…

Show ALL WORK and ANSWERS on the exam A theme park is testing a new “smart ticket” system that charges visitors differently depending on how crowded the park is.The crowd level, measured on a scale from 0 to 20, is represented by .The price of a ride ticket in dollars at any crowd level is modeled by the following piecewise function :                                            

Show ALL WORK and ANSWERS on the exam A robotics engineer is…

Show ALL WORK and ANSWERS on the exam A robotics engineer is programming the vertical movement of a mechanical arm.The arm’s “default motion profile” is modeled by the parent function:                                                                                 However, to fit the arm into a custom workspace, the engineer must apply several precise modifications to this motion model: Shift the motion 4.5 units to the left to align with the new starting position on the track. Vertically stretch the graph by a factor of 3.2 so the arm reaches higher positions more quickly. Reflect the motion across the x-axis because the mechanism inverts vertical movement. Shift the entire graph upward by 7.4 units to position the arm above an obstacle. Your Tasks Starting with the parent function, write the final transformed function after applying all four transformations in the order given. Explain (briefly) what each transformation does to the graph of the function in the context of the robotic arm’s motion.