Population Growth and Food Production in Uganda
Part A: Food Supply
Below is shown production of various grains in Uganda in the years
from 1998 to 2007. The units are in thousands of tons.
Data is from http://faostat.fao.org/site/609/default.aspx#ancor
1)
Grains
2085
2178
2112
2309
2368
2508
2274
2459
2667
2631
Grains
Grain Produced in 1000's of tons
Year
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
3000
2500
2000
1500
1000
500
0
0
5
10
15
Years Since 1995
Using your knowledge of linear functions or linear regression, find a linear model for the dataset
(years since 1995, grains).
2) What does the slope tell you about grain production in Uganda? What does the y-intercept tell you?
3) Using your model, estimate what you would expect the grain production to have been for Uganda in 2010
and 2012. Predict what the production of grain would be for Uganda in 2014.
Part B: Population
In the second part of this lesson we will consider the population growth of Uganda and then compare the models for
food production and population growth.
Below is shown is the population (in millions) of Uganda for the years from 1995 to 2009.
Year
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
Population
20.7
21.2
21.9
22.5
23.2
24
24.7
25.5
26.3
27.2
28.2
29.2
30.3
31.4
32.4
Data is from http://faostat.fao.org/site/609/default.aspx#ancor
Using the following questions as a guide, determine the equation of a model that accurately represents population of
Uganda over time.
1) Make a scatter plot of the dataset (years since 1995, population). Sketch the plot below:
2) Consider a linear model for the data set. Using your algebraic knowledge of lines or linear regression, find a
linear mode for the data set. Would you feel comfortable using your linear model to make predictions?
Support your answer using mathematics.
3) One way to think about exponential growth is to think about obtaining the y-value for a new point
(newX,newY) in the data set from another point by multiplying a constant amount by the y-value of the
previous point (oldX,oldY).
So we can write
newY = oldY * constant
That means that the ratio of consecutive y-values is constant. That is
newY / oldY = constant.
Calculate these consecutive ratios for the data given. Are these differences close to a single constant value?
4) Let’s use the average of those ratios as a possible base for an exponential model for our data set.
5) Using your work from above, compare the model in #5 to the original data set. Would you feel good about
using your model to make predictions for population? Explain.
6) In the first part of this lesson, we created a linear model for the production of grain in Uganda. How can we
compare the production of food in Uganda to the population of Uganda over time?
Population Growth and Food Production
Name _________________________________
The population of a country is initially 2 million people and is increasing at 4% per year. The country's annual food
supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.5
million people per year.
1. Based on these assumptions, in approximately what year will this country first experience shortages of food?
2. If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for
an additional 0.5 million people per year, would shortages still occur? In approximately which year?
3. If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply,
would shortages still occur?
Taken from Illustrative Mathematics
http://www.illustrativemathematics.org/standards/hs