Show that the transformation is canonical and find a generating function

One of the inventors of integrated circuits observed that the number of transistors that fit on an integrated circuit will double every 24 months. what type of relationship most appropriately models this situation?

Kevin's bank offered him a 4.5% interest rate for his mortgage. if he purchases 3 points, what will be his new rate?

Technicians have installed a center pivot, circular irrigator for a farm that covers 25 acres. a.) how long is the irrigation boom (in feet) from the center pivot to its farthest extent? b.) if the irrigation boom makes 4 full revolutions in a day, how many miles does the end of the boom travel in 5 days?