Unit 8 Math Practice
Name________________________
1) There are 300 falcons living in a certain forest at the beginning of 2013. Suppose that every year
there are 60 falcons born and 30 falcons that die.
a. What is the population growth rate (include units)? Interpret the value.
dN/dt = B – D
dN/dt = 30 falcons/year
b. What is the per capita growth rate of the falcons over a year? Interpret the value.
dN/dt = rmaxN
30 = rmax(300)
rmax = 0.1
c. Fill in the table and the construct a graph.
Year
2013
2014
2015
2016
2017
2018
Population
300
330
363
399
439
483
Graph should be (slightly) J-shaped.
d. Find the average rate of change for the falcon population from 2013 to 2018 (include units).
Slope = dY/dX
(483 – 300) / (2018-2013) = 36.6 falcons/year
2) Kentwood, Michigan had a population of 49,000 in the year 2013. The infrastructure of the city
allows for a carrying capacity of 60,000 people. rmax = .9 for Kentwood.
a. Is the current population above or below the carrying capacity? Will the population increase or
decrease in the next year?
b. What will be the population growth rate for 2013 (include units)?
dN
K N
 rmax N 

dt
 K 
dN/dt = (0.9)(49000)((60000-49000)/60000) = 8,085 people/year
c. What will be the population size at the start of 2014.
49000 + 8085 = 57,085 people
d. Fill in the following table. Then graph year vs. population size.
Year
Population size Population growth rate
2013
49000
8085
2014
57085
2496
2015
59581
374
2016
59955
40
2017
59995
4
Graph should look like “second half” of a logistic growth curve.
e. What happened to the population size over the years? What happened to the population growth rate
over the years? Population size grew each year, but the growth rate slowed substantially as the
population neared the carrying capacity.
f. Explain your answer from part (e) in terms of the biological definition of carrying capacity AND in
terms of the mathematical formula:
dN
K N
 rmax N 
 . The population growth rate slowed as it
dt
 K 
neared carrying capacity b/c resource availability decreased. In terms of the formula, the growth rate
becomes smaller each year as N approaches K.
3) There are 2,000 mice living in a field. If 1,000 mice are born each month and 200 mice die each
month, what is the per capita growth rate of mice over a month? Round to the nearest tenth.
dN/dt = 1000 – 200 = 800
dN/dt = rmaxN
800 = rmax(2000)
rmax = 0.4
4) The net annual primary productivity of a particular wetland ecosystem is found to be 8,000 kcal/m2. If
respiration by the aquatic producers is 12,000 kcal/ m2 per year, what is the gross annual primary
productivity for this ecosystem, in kcal/ m2 per year? NPP = GPP – R 8000 = GPP – 12000 GPP = 20,000
5) The gross annual primary productivity of an algal bed in the Caribbean Sea is found to be 24,345
kcal/m2. Respiration by the algae within this ecosystem utilizes 7,840 kcal/m2 per year. What is the net
annual primary productivity for this ecosystem, in kcal/m2 per year? NPP = 24345 – 7840 NPP = 16,505
6) Researchers used the mark-recapture method to estimate the number of individuals in a population.
Using the results presented in the table below, estimate the total number of individuals in the
population. Give your answer to the nearest whole number.
Number of marked individuals
Total number of individuals
Recapture Group
14
88
Entire Population
180
__1,068___