AP BIO EQUATIONS AND FORMULAS REVIEW SHEET #4 – Answer Key
Formulas:
Rate Population Growth Exponential Growth Logistic Growth
dY/dt dN/dt = B – D
Nr
dt
dN
max
=
−
=
K
NK
Nr
dt
dN
max
dY = amount of change B = birth rate D = death rate N = population size
K = carrying capacity r
max
= maximum per capita growth rate of population
Notes
dt
dN
=
t
N
∆
∆
=
timeinchange
sizepopulationinchange
= population growth rate
Example 1:
There are 300 falcons living in a certain forest at the beginning of 2013. Suppose that every year there are 50
falcons born and 30 falcons that die.
a. What is the population growth rate (include units)? Interpret the value.
dN/dt = B – D = 50 – 30 = 20 falcons/year. Each year the falcon population will increase by 20 falcons.
b. What is the per capita growth rate of the falcons over a year? Interpret the value.
Nr
dt
dN
max
=
so 20 = r
max
300 so r
max
= .067 The falcon population will increase by 6.7% each year.
c. Fill in the table and construct a graph.
Year Population
2013 300
2014 320
2015 341
2016 364
2017 388
2018 414
d. Find the average rate of change for the falcon population from 2013 to 2018 (include units). Interpret the
value.
We have two data points: (2013, 300) and (2018, 483). Average rate of change = slope
8.22
2013
2018
300414
=
−
−
=
∆
∆
=
x
y
slope
falcons/year.
Over the past five years, the falcon population has increased by 22.8 per year on average.
Example 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. r
max
= .9 for Kentwood.
