This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 1 Solutions . At and hence 17 (2010) we have .
41. The initial population is
hours we have
or
compute the population after
42. We have . Since the population doubles in
. Now we can
. Hence
hours: . So
for . We get . Now we solve the equation
years. 43. In the logistic growth equation
. To determine we use
A simple calculation give . Thus
to get
.
. Now the population in 2010 is 44. In the logistics equation
Since
ing this equation for gives and 45. Let . Then
. The equation equation together imply and . Thus
we get . Solv . Now . The equation
implies implies that
. These . Cross multiplying and simplifying leads to
. Solving
for
gives the result. Now replace the formula for
into
. Simplifying gives
. The formula for follows
after taking the natural log of both sides.
46. We have
,
, and
ing the result of the previous problem we get . Us Section 1.4
1. This equation is already in standard form with
. An antiderivative
of
is
so the integrating factor is
. If we
multiply the diﬀerential equation
by
, we get the equation and the left hand side of this equation is a perfect derivative, namely,
. Thus,
. Now take antiderivatives of both sides and
multiply by
. This gives ...
View Full
Document
 Fall '08
 BELL,D

Click to edit the document details