Practice Exam 3

Exam 3 will cover sections 4.4, 4.5, 4.6, 5.1, 5.2, 5.4, 5.5, 5.6, and the first part of section 6.1 up to page 451. Problems below referred by a number and a page number are problems from your text.

1) # 17, #19 p. 331 (Simplify as far as possible)

2) #21 p. 331 (Simplify as far as possible)

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

[Maple Math]

4) #29, # 31 p.332

5) Simplify

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

6) # 71 p. 332

7) # 31, # 33 p. 340 (You don't have to check using grapher.)

8) 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?

9) 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.

(c) If the present trend continues, when will the population reach 25 thousand?

10) 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.

11) #1, p. 405, # 25, # 37 p.406

12) # 7 p. 423, # 17, #25 p.424

13) #51, #53 p. 424

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

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

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

16) Find a possible formula for the following graphs

(A)

[Maple Plot]

(B)

[Maple Plot]

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