Comprehension
Understanding
the problem; visualizing a solution
Questions
 Do you
know the current world population? What units did you
use in this estimate?
 How much
do you think the population grew in the last 10 years?
 We will
compare the population growth in the last ten years to the growth
in 1950. How could your compare growth over different periods
of time? Compare your ideas with others in your group.
 Do you
think it would be useful to be able to predict future population?
Why?
 What do
you think are some important factors that influence population
growth?
 What do
you think are some of the important consequence of population
growth?
Acquisition
Learn or review
mathematical concepts and skills needed to study population change.
See the menu at the left.
Information
The table below gives world population for selected years.
Year

1950

1960

1970

1980

1985

1990

1995

1999

Population
(billions)

2.555

3.039

3.708

4.456

4.855

5.284

5.691

6.003

U.S. Census
Report http://www.census.gov
Application
Questions
 How much
did the population change between 1950 and 1960? What was the
average annual change for that period? State the units
clearly.
 Repeat
question 1 for the period between 1970 and 1980; between 1990
and 1995.
 Do you
think a linear model would be good for these data? Explain your
reasoning. How about an exponential model?
 Create
an exponential model. For this question, use exponential regression.
a) Plot the data on from the (t,
P) coordinate system where t = 0 in 2000 and P is the world
population at time t (in billions).
b) Use exponential regression
to derive the function which describes the world population
(in billions) at time t. Graph the function and call it P(t).
 Use the
function P(t) to answer these questions.
a) What
was the world population in 1946?
b) When did the population reach 5 billion?
c) How many years did it take for the population to increase
from 2 billion to 3 billion?
d) How many years did it take for the population to increase
from 3 billion to 4 billion?
e) How many years will it take for the population to double
its current level?
 Determine
the change in population from the beginning to the end of the
given years.
a) 1950
b) 2000
c) 2005
 The rate
of change of the population over a period of time is the
change in population divided by the change in time. Determine
the rate of change of the population for the given periods of
time. State your units clearly.
a) January
1,2002 to January 1, 2003
b) January 1, 2002 to July 1, 2002
c) January 1, 2002 to April 1, 2002
d) January 1, 2002 to January 2, 2002
Reflection
 Reflect
on the computation
a. What did you do to predict the population at a particular
time?
b. What did you do to predict when the population will reach
a particular level?
 Reflect
on the graph
a. Do you think the rate of change of population is the same
now as it was 50 years ago?
b. If you had used a linear model, what differences would that
have made in your predictions?
 Reflect
on the interpretations
a. How can you compare population change over different intervals
of time?
b. What occurrences might lead to slower population growth?