4) Professor Wei observed that students have difficulty remembering the information presented in his lectures. He modelled the percentage of information retained, R, by the function R(t) = 100e-pt,t 20, where t is the number of days after the lecture. He found that 1 day after a lecture, students had forgotten 50% of the information presented. a) Find the value of p. b) Use this model to find the percentage of information retained by his students 36 hours after Professor Wei's lecture. Based on this model, Professor Wei believes that his students will always retain some information from his lecture. c) State a mathematical reason why Professor Wei might believe this. d) Write down one possible limitation of the domain of the model.