6.8:
Growth and Decay
Law of Uninhibited Growth or Decay,
says that an amount
A
varies with time
t
according to the
model: A
(t) = A
0
e
kt
,
where
A
0
is the original amount at
t
= 0 and
k
≠
0 is a constant.
If
k > 0
, then
A
is increasing over time (growth); if
k < 0
, then
A
is decreasing over time (decay).
Newton’s Law of
Cooling,
which says that the temperature of a heated object decreases exponentially with time toward
the temperature of its surroundings:
u(t) = T + (u
0
– T)e
kt
, k < 0,
where
T
is the constant surrounding
temperature and
u
0
is the initial temperature of the heated object.
Logistic Growth Model,
which says
that growth is limited: P(t) =
c
ae
bt
1
+

, were
a, b
, and
c
are constants with
b
> 0 and
c
> 0;
c
represents the carrying capacity or maximum value that the function can attain.
1.
A culture of bacteria obeys the law of uninhibited growth.
If 500 bacteria are present initially and
there are 800 after 1 hour, how many will be present in 5 hours?
How long will it take for the
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Staff
 logistic growth model, uninhibited growth, American Bald Eagles

Click to edit the document details