Ab Review 08 Integral Worksheet - Penn State University Page 4
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511. (2012, AB-5) (No Calculator) The rate at which a baby bird gains weight is proportional to the difference
between its adult weight and its current weight. At time
t , when the bird is first weighed, its weight is
0
B t is the weight of the bird, in grams, at time t days after it is first weighed, then
20 grams. If
dB
1
100
B
.
dt
5
Let
y
B t
be the solution to the differential equation above with the 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.
2
2
d B
d B
(b) Find
in terms of B . Use
to explain why the graph of B cannot resemble the following
2
2
dt
dt
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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