Calc ab Unit 7 Progress Check mcq Questions & Answers 2024 ( A+ GRADED 100% VERIFIED)

Calc
ab
Unit
7
Progress
Check
mcq
Let
y=f(x)
be
the
particular
solution
to
the
differential
equation
dydx=ex−1ey
with
the
initial
condition
f(1)=0.
What
is
the
value
of
f(−2)
?
-
ANS
0.349
The
rate
of
change
of
the
volume
V
with
respect
to
time
t
of
water
leaking
from
a
tank
is
proportional
to
the
cube
of
the
volume.
Which
of
the
following
is
a
differential
equation
that
could
describe
this
relationship?
-
ANS
dV/dt=−0.2V^3
A
hard-boiled
egg
is
removed
from
a
pot
of
hot
water
and
set
on
the
table
to
cool.
The
rate
of
change
of
the
egg's
temperature
T
with
respect
to
time
t
is
proportional
to
the
difference
between
the
egg's
temperature
in
degrees
Fahrenheit
(°F)
and
the
room
temperature
of
75°F.
Which
of
the
following
is
a
differential
equation
that
describes
this
relationship,
where
k
is
a
constant?
-
ANS
dT/dt=k(T−75)
Out
of
a
total
of
N
students
at
a
school,
the
number
of
students
who
have
seen
a
new
television
program
increases
at
a
rate
proportional
to
the
product
of
the
number
of
students
who
have
seen
the
program
and
the
number
of
students
who
have
not
seen
the
program.
If
S
denotes
the
number
of
students
who
have
seen
the
program
at
time
t,
which
of
the
following
differential
equations
could
be
used
to
model
this
situation,
where
k
is
a
positive
constant?
-
ANS
dS/dt=kS(N−S)
Which
of
the
following
is
a
solution
to
the
differential
equation
xy′−3y=6
?
-
ANS
y=5x^3−2
Of
the
following,
which
are
solutions
to
the
differential
equation
4y+y′′=0
?
1.
y=3sin(2x)
2.
y=5cos(2x)
3.
y=e^2x
-
ANS
1
and
2
only