Part II: The Answers
376
Answers
601–700
613.
the total bird population 6 months after they’re placed in the refuge
Because p'(t) is the rate of growth of the bird population per month, p(t) represents the
bird population after t months. From the net change theorem, you have
′
=
−
∫ p t dt p
p
0
6
6
0
( )
( ) ( )
This represents the change in the bird population in 6 months. Therefore,
100 0
6
+
′
∫ p t dt
( ) represents the total bird population after 6 months.
614.
the net change of the particle’s position, or displacement, during the first 10 seconds
Because s'(t) = v(t), where s(t) is the position function of the particle after t seconds, you have
v t dt s
s
( )
( ) ( )
0
10
10
0
∫
=
−
This represents the net change of the particle’s position, or displacement, during
the first 10 seconds. Notice that because the velocity is in meters per second, the
displacement units are in meters.
615.
the net change in the car’s velocity, in meters per second, from the end of the third second
to the end of the fifth second
Because v'(t) = a(t), where v(t) is the velocity function of the car after t seconds,
you have
a t dt v
v
( )
( ) ( )
3
5
5
3
∫
=
−
This represents the net change in the car’s velocity, in meters per second, from
the end of the third second to the end of the fifth second.
616.
the total number of solar panels produced from the end of the second week to the end of
the fourth week
Because P'(t) is the rate of production per week, P(t) represents the total number of
solar panels produced after t weeks. By the net change theorem, you have
′
=
−
∫ P t dt P
P
2
4
4
2
( )
( )
( )
This represents the total number of solar panels produced from the end of the
second week to the end of the fourth week.
617.
the net change in the charge from time t 1 to time t 2
I(t) is defined as the derivative of the charge, Q'(t) = I(t), so by the net change
theorem, you have
I t dt Q t
Q t
t
t
( )
( )
( )
1
2
2
1
∫
=
−
This represents the net change in the charge from time t 1 to time t 2 .