1. Open an Excel file and construct a scatterplot using the data gathered in step 6 of your preparation. Create a column in the table to zero out the years to make \"years since 1800\" the independent variable and Population (in billions) the dependent variable. 2. From looking at the pattern of the data points, which type of model do you think will work best? 3. On your scatterplot, insert a linear trendline, its equation and its r2 value. Record the equation L(t) and r2 below: a. Identify the slope of the linear model and explain its meaning in context. b. Identify the y-intercept of the linear model and explain its meaning in context. 4. To write an exponential model by hand, we need to know the annual percentage growth rate, r. Use the current yearly growth rate found in #4a of your prep work to write an exponential function expressing population P as function of time, t, since the year 1800 when the population was just under 1 billion. Ask your instructor to check this answer as you will need to use it later. 5. Return to your scatterplot. Insert an exponential trendline, its equation E(t) and r2 and record them below. 6. Which of Excel's models is better? The linear model found in #3 or the exponential model found in #5? Justify your answer. - 54 7. Now compare the two different exponential models we have. Find the predicted population value for the year 2000 using the equation you wrote in #4 using the 1.14% growth rate and the one Excel calculated in #5 using the number e. Exponential model written by hand (question 4)? 2000: P(200) = ____________________ Excel's exponential model (question 5)? 2000: E(200) = ____________________ 8. Which of the equations gives an output closer to the actual population in 2000? 9. The World Population Clock indicates that the growth rate is declining, estimating that it will be 0.5% by around 2050. It also indicates the 2040 population will be around 9 billion. Use this information to write an exponential equation for the population, Q, for t years after 2040. 10. The total land mass of the world is a bit more than 57,000,000 square miles. Suppose that (1) all of this land is inhabitable/usable (it isn't) (2) that one square yard is required to support each human on earth (which means we'll eat a lot of algae in our high-rise apartments). Based on these assumptions, to the nearest billion, what is the maximum population the world could support? 11. Use Goal Seek to estimate when this maximum population might be reached using the new exponential equation Q(t) that you wrote in #9. 12. Summarize what you learned from this activity. Write a brief well-written paragraph discussing world population, exponential growth, carrying capacity, or any other topics covered in this activity that were of interest to your group. You may refer to the opinion articles in the preparatory portion of this lab or do additional research on the topics above. You may attach a separate page if needed