BC Calc III
DE Quiz
Name:
Calculator not allowed.
You must show enough work so that I can recreate your results.
#1.
a. Write a differential equation (Initial Value Problem) describing the temperature
as a function of time of a can of soda taken out of a 40  F refrigerator and left in a
65  F room.
b. Make a sketch of the solution to the above Initial Value problem. Mark the
scale on the temperature axis clearly. You do not need a scale on the time axis.
Temp
time
#2.
Solve the following differential equation using separation of variables.
y   y 2 x( x 2  2)4
BC CALC III
#3
A national park in Tanzania can sustain a population of water buck of about 800.
After several years of drought, the population was only 100, but now is beginning
to grow logistically again. (Let this be time t = 0.)
a. Express the differential equation for this situation (in terms of k).
The solution to this differential equation is given by: P 
C
de
 kCt
1
, where
P = number of water buck at time t (in years).
b. Find the constant of integration d.
c. Four years later the population had grown to 300. Find the constant k. [Your
answer should involve a natural log].
d. What will be the population of water buck when the population is growing
most rapidly?
e. What would happen to the water buck if their population was 900 at some
point? Explain your answer making explicit reference to the Differential
equation.
BC CALC III
Match each slope field with the correct differential equation.
(a)
(c)
(e)
(g)
BC CALC III
(b)
(1)
y  xy
(2)
y  x  y
3)
y  x  (2  y )
(4)
 y 
y  sin 

 3 
(5)
y 
(6)
y  x 2
(7)
y  y 2
(8)
  y2 
y  sin 

 2 
(d)
(f)
1
( x  2)( y  3)
2
(h)