Practice Exam 3

Below is a list of problems that should help you study for the exam. Problems referred by a number and a page number are problems from your text.

1) # 51, # 67 p. 285

2) Express as a single logarithm and simplify as far as possible

[Maple Math]

3) #21 p. 295 (Simplify as far as possible)

4) Simplify

(a) [Maple Math] (b) [Maple Math]

5) # 71 p. 295

6) # 17, #39 p.302 (You do not have to check your solution on a grapher unless you want to.)

7) A radioactive element decays exponentially according to the formula

[Maple Math]

for some constants [Maple Math] and [Maple Math] . Time t is measured in days. The initial amount of 50 grams at [Maple Math] decays to 40 grams in 10 days.

(a) Find the half-life of the element.

(b) When will the amount be 10 grams?

8) The population of a town, [Maple Math] , in thousands, increases according to the formula

[Maple Math] ,

where [Maple Math] is the time in years since Jan.1, 1990.

(a) What will the population be on Jan 1, 2005?

(b) Find the doubling time of the population.

9) A forester is standing 200 ft from the base of a tree. He measures that the angle of elevation from the point he is standing to the top of the tree is 0.68 radians. Find the height of the tree.

10) #1, p. 369, # 17, # 23 , # 27 p.370

11) # 25, #37 p. 387

12) #51, #53 p. 388

13) Suppose that the angle t is in the II quadrant. Suppose sin(t)=0.3. Find cos(t), tan(t), cot(t), sec(t).

14) Determine the amplitude and the period of the following functions:

(a) [Maple Math] (b) [Maple Math] (c) [Maple Math]

15) Find a possible formula for the following graphs


[Maple Plot]


[Maple Plot]

("Pi" stands for [Maple Math] .)