Question

3. The United Nations' Department of Economic and Social Affairs stated in 1999 that the world's population stands at 6 billion and is growing at 1.3% per year, for an annual net addition of 78 million people." a. This statement contains two descriptions of predicting world population growth that contradict each other. What are the two descriptions and why are they contradictory? b. Using the information in the statement, construct a linear model for world population in billions in terms of years from 1999. Define your variables. c. Using the information in the statement, construct an exponential model for world population in billions in terms of years from 1999. Define your variables. d. Complete the table for the two models you have constructed Years Years from 1999 Population from linear model (billions Population from exponential model (billions) 1999 2000 2001 2002 2005 2010 e. In your table you should see that the models have the same prediction for two years. Why is this the case? (If you don't see this, go back and check your work!) f. Which model predicts larger populations after the year 2000? Why does this make sense? 116 1. Without using a graphing calculator, match the equations and graphs. Explain your reasoning. f(x)-2(1.3') gx) 21.8') 2. The equation 3-2 2x+5 cannot be solved using an algebraic method. However, you can use a table and a graph as you did in class. In those problems, you found the point of intersection of an exponential function and a horizontal line. Notice that the right side of this equation can be seen as a line with slope 2. This fact will change what the graphs of the functions look like together: there will be 2 points of intersection! a. Use your graphing calculator to graph the functions f(x)-3.2' and g(x)-2x+5. Create a graph of these functions on the grid here. b. What are the two intersection points (x, y) of f and g? Give answers accurate to 4 decimal places. c. What are the solutions to the equation 32'-2x+5 d. Create tables for fand g and use the tables to show estimated solutions of the equation 3.2-2x+5. What should you be looking for in the tables?

Answer 1

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