Please show all work.The following problems are applications. You must respond in full sentences to receive full credit. You are graded not only on obtaining the correct values, but in the completeness and presentation of your results. Kappa Airlines has projected the percentage of young adults booking ights on their airlines to rise in the next few years. The following model gives their projection of the percentage of young adult passengers in year t, with 0 S t S 5. t2+3t+6 p(t)_50(t2+6t+12) These young adults usually pick shorter ights, pick less expensive tickets, and order less expensive items from the in-ight services. Kappa Airlines estimates that the average amount of money R spent per passenger on their ight at a percentage p of young adults is: p + 6 R = 0 (p) 50 (p + 3) Answer the questions which follow: a) Calculate and explain. Evaluate p(3) and explain the interpretation with re- gards to Kappa Airline's models. b) Calculate and explain. Evaluate R(30) and explain the interpretation with regards to Kappa Airline's models. c) Find the function which represents the rate at which the money spent per pas- senger on a ight will be changing t years from now. Find this rate after 4 years