Separable Differential Equations Worksheets Page 7
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7Calculus Maximus
Notes 5.1: Separable Diff EQ
Finish Strong!
Example 12:
AP 2012-5
The rate at which a baby bird gains weight is proportional to the difference between its adult weight and its
( )
t = 0
, when the bird is first weighed, its weight is 20 grams. If B t
current weight. At time
is the weight
of the bird, in grams, at time t days after it is first weighed, then
dB
(
)
1
=
100 − B
.
dt
5
( )
( )
Let y = B t
be the solution to the differential equation above with initial condition B 0
= 20 .
(a) Is the bird gaining weight faster when it weighs 40 grams or when it weighs 70 grams? Explain your
reasoning.
d
B
d
B
2
2
(b) Find
in terms of B. Use
to explain whey the graph of B cannot resemble the following
dt
dt
2
2
graph.
( )
(c) Use separation of variables to find y = B t
, the particular solution to the differential equation with
( )
initial condition B 0
20 .
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