7. {0.53/2 Points] - PREVIOUS ANSWERS ASK YOUR TEACHER At the time the rabbit population on the island in the previous problem reaches 7000, the population learns to live with the foxes. The rabbit population is then modeled by the function S(t) = 500(1 e'o-o'\") + 7000 Where 5 represents the number of rabbits and t is the time in months. at What is the initial population according to this new model? Rabbits b What is the rabbit population at time t= 3 months? :] Rabbits c What is the rate at which the rabbit population is growing at t= 3 months? :] Rabbits/month dt Find the following limit: I' S t = Rabb't b n :1 .5 Discussion Point: What does this limit tell you about the rabbit population on this island? 8. MW] - Radioactive substances decay exponentially according to the model 00:) = 00 ekt Carbon-14 is a radioactive isotope of carbon and has a half-life of 5730 years. ASK YOUR TEACHER at If an initial amount of 00 were left to decay, how much would be left after 5730 years (the half-life)? Your answer will include a Qot bt Use the half-life to set up an equation to solve for the exponential constant, K Your answer will be an equation and include Qa- ct Solve the above equation for kt Round your answer to 5 decimal digitst