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Unformatted text preview: NAME Oct. 30, 2002
Teacher Section 3 MATH 115—Exam 2 Write your name, your teacher’s name and your section number on each answer sheet. Answer problem 1 in the
spaces provided on this sheet and each of the remaining numbered problems on a separate answer sheet (see
directions before each problem). In order to receive full credit for a problem you must show appropriate work.
At the end of the exam, place the answer sheets in order and put this sheet on top. No calculators or audio devices are allowed. Answer Problem 1 in the spaces provided below. (7) l. a. Find g'1(x) if g(x) = 3x5 + 7 . How would you prove that your function is the inverse off? (You do
not have to carry out the proof.) (3) b. Draw the graph of the equation. x2 — 4 y2 = 25. On your graph label all intercepts and vertices with
their coordinates, show asymptotes (if any) with a dotted line and label any asymptote with an
equation. Don't forget to label axes. Please turn over for Problems 2-6.
3—page 1 of 2 Answer Problem 2 on Answer Sheet 2. (10) 2. a. Sketch the graph of the function f(x) = —(x — 2)(x - 1)2(x + 3)2 . On your graph label the intercepts with their coordinates or values and show any asymptote with a dotted line and label it with an equation
or intercept value. Label the axes. b. In a developing country, one model for the population growth of a city after t years is C(t) = -2-(1.7)t (in thousands). The growth of population in a rural area after t years is modeled by R(t) = 5(0.9)t
(in thousands). (s) i. Draw the graphs of C and R on the same coordinate axes. Label graphs clearly with the names of
their functions (C, R.). Label intercepts with their values and show clearly any asymptote.
(2) ii. What is the meaning of the point of intersection for these models? Answer Problem 3 on Answer Sheet 3.
(14) 3. Let —— (x+1)2 .
b. Find each of the following for the graph off.
0. Draw the graph off Answer Problem 4 on Answer Sheet 4.
4. a. Evaluate each of the following: 02) i. log256—log27 ii. 271°g32 iii. 1n(JE)+1n1 (7) b. Let g(x) = log4(x + 16). (i) Find the domain of g and (ii) draw the graph of g. On your graph show
any asymptote with a dotted line labeled with its equation or intercept. Label the intercepts with
their coordinates or values. Label axes. Answer Problem 5 on Answer Sheet 5.
5. a. Suppose log x = —l.1, log y = 2.3 . Evaluate each of the following. Don‘t just give a numerical
answer; indicate clearly in the steps the log rules you used. (8) i. 1041—36-6) ii. log(x2y)
(s) b. Write as a single logarithm and simplify: ln s — 2 In (t 2 + 1) + %1n (25) Answer Problem 6 on Answer Sheet 6.
6. Find all real solutions to the equations:
(8) a. 7(1+2x—3)=21 ,(8) b. 1—4ln(3—x)=0 End of Examination 3~page 2 of 2 ...
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