Handout One                 Math 375                             Uhlenbeck                                        Due Monday, Sept 11

NAMES________________________________

_______________________________

______________________________
 
 
 

1. Suppose that a trap that is assumed to catch 1% of the mosquitoes
is monitored after a rain, and the data collected are
 

Day one (6:30 PM) 151 mosquitoes

Day two (7:30 PM) 306 mosquitoes.

The difference in the two times is ignored and the biologist also
notices that the one number is about twice the other. She uses this
approximation of one day, and 150 for the first number and 300 for
the second. How many mosquitoes does she expect to find on the third
day (assuming they are increasing exponentially).? How many
mosquitoes does she predict that there are.

2. Now redo problem 1 using the exact numbers. Is the prediction of the
number of mosquitoes significantly different?

3. Suppose the doubling time in dry weather is known to be 70 hours.
How many mosquitoes would you guess would be in the trap the second day
if 294 were found the first day? How should you check your answer?

4. Suppose the doubling time in dry weather is three days in the
absense of frogs (using a sensible approximation for the data in 3).
Suppose we also start with 300 mosquitoes found the first day.
How many would the frogs have to eat a day to keep that number fixed?

(Assume the model dN/dt = kN - C).
 
 

5. A reasonable model for preditors (say frogs) fed a fixed amount of food
would be

dN/dt = -kN + F

where k would represent the rate the frogs to die off with no
food, and F would be the fixed food fed to them daily. Discuss the
solution of this equation with k=.5 and C = 6.3. What are the
units? Where does the model not make any sense? (N = 0?)