1 Wed. Aug 20            Exploration 1

 

2 Thurs. Aug 21           p. 91 #3, 4

 

3 Fri. Aug 22                p. 91 #5, 7, 9

 

Long Due 8/25            p. 91 #4

 

4 Mon. Aug 25 p. 91 #1, 2, 8

Extra Problems not in your book

 

1.      A pendulum hangs from the ceiling.  As the pendulum swings, its distance, d cm, from one wall of the room depends on the number of seconds, t, since it was set in motion.  Assume that the equation for d as a function of t is  for .  It is desired to find out how fast the pendulum is moving at a given instant, t, and whether it is approaching or going away from the wall.

 

a.       Find d when t = 5.  If you don’t get 95 for the answer, make sure your calculator is in radian mode.

b.      Estimate the instantaneous rate of change of d at t = 5 by finding the average rates for t = 5 to 5.1, t = 5 to 5.01, and t = 5 to 5.001.

c.       Why can’t the actual instantaneous rate of change of d with respect to t be calculated using the method in part b?

d.      Estimate the instantaneous rate of change of d with respect to t at t = 1.5.  At that time is pendulum approaching the wall or going away from it?  Explain.

e.       How is the instantaneous rate of change related to the average rates?  What name is given to the instantaneous rate?

f.        What is the reason for the domain restriction ?  Can you think of any reason there would be an upper bound to the domain?

 

2.      A tire is punctured by a nail.  As the air leaks out, the distance, y inches, between the rim and the pavement depends on the time, t minutes, since the tire was punctured.  Values of t and y are given in the chart below.

 

t min

0

2

4

6

8

10

12

14

y inches

6.00

4.88

4.42

4.06

3.76

3.50

3.26

3.04

 

a.       About how fast is y changing at t = 2, t = 8, t = 12?

b.      How do you interpret the sign of the rate at which y is changing?

 

5 Tues. Aug 26             No assignment given, but it should have been look at 2004 AB1 and figure out which questions you know how to answer.

 

6 Wed. Aug 27            p. 378 #15, 16 with counting boxes, Extra Problem #3

            Extra Problem #3 (Foerster p. 17 #9)

You have been hired by an automobile manufacturer to analyze the predicted motion of a new sports car they are building.  When accelerated hard from a standing start, the velocity of the car,  ft/sec, is expected to vary exponentially with time,  seconds, according to the equation .

a.       Draw the graph of the function  in the domain [0, 10].

b.      What is the range of the velocity function?

c.       Approximately how many seconds will it take the car to reach 60 ft/sec?  You might try turning on your grid feature.

d.      Approximately how far will the car have traveled when it reaches 60 ft/sec?

e.       At approximately what rate is the velocity changing when ?

f.        What special name is given to the rate of change of velocity?

 

7 Thurs. Aug 28           p. 378 #1, 12a, 13, 15, 16 (this time do all problems with trapezoids instead of rectangles).

 

Long Due 8/28            p. 91 # 9

                                    p.91 # 2, Extra Problem #1

Exploration 1 is due on 8/28 as well.

 

8 Fri. Aug 29                p. 378 #3, 5a, 7, 8, 10 (again we are doing trapezoids).

 

Long Due 9/2              p. 378 #15, Extra problem #3

                                    p. 378 #12a, 16

                                    p. 378 #5

Exploration 3 is due on 9/2


9 Tues. Sept 2              p. 102 #11, 12, 15 – 18, 19 – 22

 

10 Wed. Sept. 3           p. 102 #1, 2, 4, 6, 13, 14, 33, 35

 

Long Due 9/4              p. 102 #11, 16

                                    p. 102 #20, 1

                                    p. 102 #6, 14, 35

 

11 Thurs. Sept. 4          Exploration 6, p. 122 #1, 3, 5, 7, 8