LINEAR GROWTH
N(t) = No + rt
20
No = 10
r = 2 persons/hour
t = 6 hours
N(t) = 10 + (2 x 6) = 22
Exponential Growth
N(t) = No ert
Each guest invites 2 friends
each of them invite 2 friends …
Logistic Growth
N(t) = K / (1 + be-rt)
Eventually, your room fills up
K = carrying capacity
people
Linear Growth
25
15
10
5
0
0
1
2
3
4
time (hours)
5
6
EXPONENTIAL GROWTH
Find the final population after 20 years
starting from a population of 15,000 with
a growth of rate of 19 per thousand per
year
N(t) = No ert
No =
e =
r =
t =
EXPONENTIAL GROWTH
Find the final population after 20 years
starting from a population of 15,000 with
a growth of rate of 0.019
N(t) = No ert
No = 15000 persons
e = 2.718281828459045…
r = 0.019
(1.9% 19 /thousand [persons per year])
t = 20 year
Keystrokes
20
*
0.019
=
0.38
C
2.718281… e
x^y
0.38
=
1.46228…
*
15000
=
21,934.2…
LOGISTIC GROWTH
N(t) = K / (1 + be-rt)
b = ln [(K - N0) / N0]
K = 50,000 (carrying capacity)
N0= 15,000
KEYSTROKES
50000
15000
=
/
15000
=
ln =
2.3333…
0.84729… (b)
20
*
0.019
=
0.38
35000
C
(r*t)
C
2.718281…
x^y
-0. 0.38
+/=
*
0.84729…
=
+
1
=
1.579429
50000
/
1.579429
=
31,657
683861…
0.579429…
C
http://www.life.umd.edu/classroom/biol106h/L28/L28_popeco.html