Part B: Full Solution Read each question carefully. Provide full solutions in the space provided 1) It costs a bus company $225 to run a minibus on a ski trip, plus $30 per passenger. The bus has seating for 22 passengers, and the company charges $60 per fare if the bus is full. For each empty seat, the company increases the ticket price by $5. How many empty seats should the bus run with to maximize profit from this trip? [6 marks] 2) After 10 days, 95% of a radioactive material has decayed a) What is the halflife of the material? [2 marks] b) How long will it take for there to be 15% of the original material left?[2 marks] 3) Determine the equation for the sinusoidal function below. You may choose to state your answer as either a sine or cosine function. [4 marks] \f5) A weather balloon is spotted from two angles of elevation, 57 and 83, from tracking stations A and B in the diagram below. The tracking stations are 15 km apart. Determine the distance from tracking station A to the balloon, rounded to the nearest kilometre. [4 marks] 6) The fifth term of a geometric series is 405 and the sixth term is 1215. Calculate the sum of the first nine terms. [6 marks] 7) Marisa has just won a contest. She must decide between two prize options: Option A: Collect a lumpsum payment of $50 000. Option B: Receive $800 at the end of every quarter for 10 years from an investment. The investment earns 80/o/annum, compounded quarterly. How much more money would she have if she chooses the lump sum? [6 marks] 8) Prove the following trigonometric identity. [4 marks] (sec x) (secx) = csc(x) sec(x) tan x