All answers should be written out in complete sentences, and all claims should b

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All answers should be written out in complete sentences, and all claims should be supported with careful reasoning, explained as completely as possible. You may either submit a hand-written report, a typed report, or any combination. Feel free to draw sketches (by hand is fine) if it seems useful to support your arguments. You might find it useful to use Excel (or a similar spreadsheet program) to calculate and display your tables. You may work on this project collaboratively, but each student must hand in an individual write-up In this project, we study how quickly the US population is growing. The United States Census has a population clock at http://wwv.census.gov/popclock/On that page, you can look up the US population on any date since the last national census in 2010. You may also notice the prominent display near the top of the page showing the current rate of growth of the US population. For example, on January 30. 2016. the population was increasing at a rate of one person every 17 seconds. We will use this census population data to estimate the rate of growth of the US population on July 4. 2015. One year. Compare the populations on July 4. 2014 and July 4. 2015. How much did the population increase during that year? Express the change as a number of people per year. Six months. How much did the population increase in the six months from January 4. 2015 to July 4. 2015? What was the rate of growth over the six months, in units of people per year? Compare your answers in the previous two questions. Explain why they are the same or why they are different in terms of the how the population was changing in the period from July 4. 2014 to July 4. 2015. The rate of growth you have just computed is an average rate of change, which is computed over an interval of time [t1, t2]- The average rate of change of population P over the interval [t1, t2] is defined by the following familiar formula: average rate = change in population/change in time = P(t2) - P(t1)/t2 - t1 However our goal was to find the rate of growth at one specific instant of time. The formula above cannot be used directly to find the rate at one specific instant, because it would lead to a fraction of the form 0/0.

Explanation / Answer

1)   Population on July 4, 2015 : 321, 442, 019

      Population on July 4, 2014 : 318, 931, 461

      Increase = 2,510,558/ year

     Average Rate = .787%

2) Population on July 4, 2015 : 321, 442, 019

    Population on Jan 4, 2015 : 321, 442, 019

Increase = 1,138, 248

    Rate = .00355% for 6 months = .0071% annually

3) Answers are different beuase, population grows continuoulsy over time

   To find growth rate, we need to use P = P0ert where P = Population at time t, P0 = initial population.

   Solving, the rate of growth = .00784%

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