Download Exponential vs Logistic Growth Activity 2016

a) A population will grow when (b>d, b<d,
b=d)
b) A population in an environment with
unlimited resources will grow
(exponentially, logistically)
c) If a population grows at a rate of N=2t,
where t is the sampling time interval,
what is N at sampling time 10?

Obtain 5 bags representing bacterial population
at different time intervals (measured in military
time).

Just by looking at the bag, can you predict the
type of growth demonstrated by the population?

Count the # of individuals at each time interval.
Graph.

Using the graph you created, predict the
population size at 1600.
 Under
what conditions will a population
increase exponentially? Be specific.
 How
can you identify exponential growth
on a graph?
 Can
we represent this growth pattern
mathematically?
 Consider
the human population graph.
Based solely on the graph, what would
you predict the human population will be
in 2100?
 Do
you think this prediction is accurate?
Explain your thinking.
 Obtain
10 bags representing the size of a
population at a given time interval
 Count
the # of individuals at each time
interval. Graph.
 Can
you identify the carrying capacity of
the environment?
• If so, mark it with a red dotted line on your graph
• If not, write a brief explanation why not
 What
is occurring at each time interval?
Generate some possible explanations.
 Can
you think of any examples of species
that have this kind of population growth
pattern?
 Create
a model of what is occurring with
your species over the 10 (weeks, months,
years). Include possible scenarios that
explain the changes in population size in
the broader context of the 10 time
frames.
 No
population can increase indefinitely
• Environment sets limits
 Maximum # of individuals a population
can support indefinitely = carrying
capacity (K)
•
S-curve
•
Takes into account carrying capacity:
▫ dN/dt = rN [(K – N)/K ]
•
When the # of individuals is small, [(K –
N)/K ] is almost 1
▫ Environment doesn’t keep population
in check
•
As N increases to near carrying capacity,
[(K – N)/K ] approaches 0
▫ Growth decreases
•
Populations may rise temporarily above
K
▫ Drop down to below K
▫ Population crash
 Examples:
• Predation
• Disease
• Competition
 What
do you think will happen to a
population of insects that are introduced
to a new environment? Justify your
prediction