AP Classroom Unit 7 Calculus well elaborated 2025

AP Classroom Unit 7
Calc
Let y=f(x)y=f(x) be the
particular solution to
the differen-
tial equation dydx=ex 1ey-
0.349
dydx=ex 1ey with the initial condition
f(1)=0f(1)=0. What is the value of f( 2)f( 2)
?
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. dVdt= 0.2V3
Which of the following is
a differential equation that
could describe this
relationship?
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 TT with
respect to time tt is
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, AP Classroom Unit 7
Calc
proportional to the
difference between the
egg's temperature in
degrees Fahrenheit
(°F°F) and the room
temperature of
75°F75°F.
dTdt=k(T 75)
Which of the following is a
differential equation that
describes this
relationship, where kk is a
constant?
Out of a total of NN 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 dSdt=kS(N S) of students who have not
seen the program. If SS denotes the number of
students who have seen the program at time tt,
which of the following differential equations
could be used to model this situation, where kk
is a positive constant?
Which of the following is a
2/6