Population Calculation Worksheet Practice Problems by dou12761

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									                                                                Population Calculation Worksheet
Here are some handy equations to help you with the problems on the back of this sheet. You will need to be
familiar with the equations for your test and the AP exam.

1. Population density:
       ����������������������������������������                                                                                               270,000������������������������              ������������������������
                            = ���������������������������������������� ����������������������������                                     for example: 9,166,605�������� �������� = 29
            ����������������                                                                                                                                        �������� ��������


2. Birth or Death Rates:
           # �������� ���������������� �������� �������� ���������������� �������� ������������ ����������������
                                                                     = �������������������� �������� �������������������� ����������������
                       �������������������� ����������������������������������������

                                           23,452 ���������������� ��������
           for example: 942,721 ������������������������ = 0.025 = 2.5 �������������������� ����������������

3. Finding Population Growth Rate (r):

             ���������������� ��������−���������������� ��������                                                                                  20,000 ���������������� ��������−15,000 ���������������� ��������
                                             = ����                                                     for example:                                                    = 0.01 = 1.0%
           �������������������� ����������������������������������������                                                                                         500,000 ������������ ������������


4. Exponential Growth
��������
     = ��������         (Derived) Nt = N0(1+r)t
��������

           for example: Initial Population of 20 with an intrinsic rate of growth of 10%
                           ��������
                  Time 1: 1 = 0.10 * 20 = 2             2 + 20 = 22 (population in Time 2)
                                              ��������
                           Time 2:                   = 0.10 * 22 = 2.2                                2.2 + 20 = 24.2 (population in Time 3)
                                               1
                                              ��������
                           Time 3: 1 = 0.10 * 24.2 = 2.4       2.4 + 24.2 = 26.6 (population in Time 4)
                           ***Can also add a ‘1’ to the growth rate so the second addition step isn’t needed
                                  ��������
                           Time 4: 1 = (1+0.10) * 26.2 = 29.282 (population in Time 5)

           Derived:                          Time 8: N8 = 20 * (1+0.10)8 = 42.871 people


5. Finding the Doubling Time of a Population: THE RULE OF 70!!!
                         70%                                           0.7
                                                  �������� ���� (�������� ����������������������������                = �������������������������������� ���������������� (��������������������)
           ���� (�������� ���������������������������� ���������������� )                                    ���������������� )

                                           0.7
           for example: 0.07 = 10 ��������������������



                                                                                      Practice Problems
Schushsville is an island of 5000 square miles off the coast of Northville. There are currently 250,000
inhabitants of the island. Last year, there were 12,000 new children born and 10,000 people were recorded as
deceased. It is believed that the island could support a population as dense as 150 people/square mile.
1. What is the current population density and what do you expect will happen to the density as time goes on?
      Current population is 250,000 people and the area of the island is 5000 sq miles, so the
                        250,000������������������������
            density is 5000 �������� �������������������� = 50 people per square mile. The population is increase, so the
            density will increase as well.


2. What are the birth and death rates?

      Birth rate = (# of individuals born) / (Total Pop.) =
      Death rate = (# of individuals who died) / (Total Pop.) =
      Currently there are 250,000 people, but how many are born, we don’t know. We do know that 12,000
           kids were born last year, but what was the population. To find last year’s population we first need
           to find out how much it change by. If only 10,000 people died last year, while 12,000 were born,
           then the population grew by 2,000 people (assuming no immigration or emigration). So
           subtracting 2,000 people from the current population, yields 248,000 people for last year’s
           population.
      Birth rate = 12,000 / 248,000 = 0.048387 or 4.83%
      Death rate = 10,000 / 248,000 = 0.040323 or 4.03%


3. What is the population growth rate (r)?

                                     ���������������� ��������−���������������� ��������
      Growth rate (����) = ��������������������                                 = (12,000 – 10,000) / 250,000 = 2,000/250,000 = 0.008 = 0.8%
                                             ����������������������������������������


4. In what year will the population of Schushville double?
                                                  0.7
      �������������������������������� ���������������� =                                        = 0.7 / 0.008 = 87.5 years
                                    ���� (�������� ���������������������������� ���������������� )



5. In what year will Schushville reach it’s carrying capacity (k)?
      Carrying capacity is when the population reaches 150 people per square mile or 750,000 people.
         Using Nt = N0(1+r)t where Nt = 750,000, N0 = 248,000, and r = 0.8% or 0.008
           750,000 = 248,000 * (1 + 0.008)t
           3.024 = 1.008t                  →               LN[ 3.024 = 1.008t]
           1.106 = 0.007968t
           T = 138.87 years


6. Is there a limit to the world’s and/or U.S. population? What factors prevent populations from growing at
their biotic potential?
      Limiting factors such as food, water, shelter, and disease prevent the population from growing at
      its biotic potential. As the world population gets closer to its limiting factor the growth rate will
      continually slow, then either stop or even become negative.

								
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