(Calculus can be used in quantitative psychology! Here's an example. ) Suppose a rumor starts spreading in a certain population. Under certain circumstances, the rumor spread can be modelled according to the equation 1 t: p() 1+ae'k' where p(t) represents the proportion of the population that has heard the rumor at time r (so if 80 percent of the population has heard the rumor at time t, then we'd have p0) = 0.8), and a and k are positive real constants. (a) Find the limit limHm p(t) and interpret your answer in terms of the model - what does this quantity represent? (b) Find the rate of spread of the rumor as a function of time t. (C) (Use a graphing calculator or Desmos or something similar.) Graph p for the case a = 10, k = 0.5 with I measured in hours. Estimate how long it takes for 80 percent of the population to have heard the rumor. Explain your work