1. (80 points) Demonstrate and Explain: Clearly and thoroughly explain your answers to these questions based on the work you did with your group on labs this week. These questions refer to Lab 10A: Population Curves. Recall, the world population in 1999 was approximately P0 = 6.067 billion people. In 2000, it was approximately P1 : 6.145 billion people. (3.) (Parts 10: 85 2a) Show how to model the world population with an exponential curve, P(t) (including how you nd the value of 7'0), and with a logistic growth curve, L(t) (where K : 15 and '1'}, 2 0.022.) (b) (Parts 1b 63' 2b) Create an accurate, well-labeled graph that shows the world populations predicted by both P(t) and L(t) from 1999 to 2049. (c) (Parts 103 63 20!) According to each of these models, how fast (in billions of people per year) is the world population growing in 2019? In 2049? Show very clearly how you are nding these solutions. (d) (Part 3) Compare the two models P(t) and L(t). As it gets large (e.g. the year 2099), what do P'(t) and L' (it) tell you about how each of the models is growing? Which of these models do you nd more realistic? Explain your reasoning