1. (80 points) Demonstrate and Explain: Clearly and thoroughly explain your answers these questions based on the work you did with your group on labs this week. These questions refer to Lab 10: Population Curves. Recall, the world population in 1999 was approximately Po = 6.067 billion people. In 2000, it was approximately P1 = 6.145 billion people. (a) (parts la and 2a): Show how to model the world population with an exponential curve, P(t) (including how you find the value of ro), and with a logistic growth curve, L(t) (where K = 15 and ro = 0.022.) (b) (parts 1b and 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 ld and 2d): 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 finding these solutions. (d) (part 3) Compare the two models P(t) and L(t). As t gets large (e.g. the year 2099), what does P'(t) and L'(t) tell you about how each of the models is growing? Which of these models do you find more realistic? Explain your reasoning