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Math 1090.04 Exam 03 Spriiig 2013 Name SthOn Student ID Number: Instructions: o Please remove headphones and hats during the exam o Show all work, as partial credit will be given where appropriate. Calcu lator work should be your final step. If no work is shown, there may be no credit given. • All final answers should be written in the space provided on the exam and in simplified form. If asked for an exact solution give the fraction or symbolic solution, do not evaluate with a calculator. o Scientific Calculators are permitted on this exam. Graphing, Programmable and Cell Phone Calculators are not allowed. • This is a “closed notes/closed book” exam You are not allowed any outside aids during this exam. If you have papers at your desk during the exam you will be given a zero on the exam. - • If your phone is out during the exam it will be considered a cheating offense put your phone away! - Exam 03, Page 2 of 7 MathlO9O.004 19 April 2013 WRITE YOUR ANSWERS ON THE LINES PROVIDED 1. Given: f(x) = , g(x) 3 x ./x2 = + 1, and Ii(x) = (a) Find (fog)(x) (a) (°( 1 cutJLA (x (b) Find h(f(g()) - (b) 1x2t 2 Z (x i LryL onsuYV I )/2 — (1—i (c) Find f(g(3)) =(z (c) p-L l - (d) Find ( - (f — x (-2( g)(2) - (d) j0 j)eJA: (y -- C V bJ — II Si - 7 >< Ii C— Cl] V + I 1+ — c’i 37 >< >( ‘ S7 37 17 ii - Cl] . Cl] j •C V Cl] V - -4- - cD II I H ‘—C V rfl 1’ rfl X x I” - LI ? :j t?tkzai H i1ir 47 - T - ‘A OD IViath 1090.004 3. (a) -I Exam 03, Page 4 of 7 i. Graph the function f(x) = 19 April 2013 3’ I 3 0 3 1 2 ii. Write the equation for the asymptote of this function 1].. (b) i. Graph the function g(x) = 2 3’ + 1 If you choose to graph intermediate functions, label your solution clearly. pb II CtY L \ b cCA0r (oI) (i 3 jz/ c2 — C a (& (-I, 1 ji ii. Write the equation for the asymptote of this function j1 11. 4. i. Graph the function h(x) (a) 19 April 2013 Exam 03, Page 5 of 7 MathlO9D.004 = x) log ( 9 : -I 20 23 ii. Write the asymptote for this function ii. (b) — (r + 1) 2 9 i. Graph the function k(x) = 1og If you choose to graph intermediate functions, label your solution clearly. — -10------- sh\4- LoD( b 2 z: (2, 1 CO H : 0t nt3: eofl x=,—I -- I__I — ii. Write the asymptote of this function ii. 7’-;-. Exam 03, Page 6 of 7 MathlO9O.004 19 April 2013 (a) Expand the following expression completely using the properties of logarithms: 5. ) (a) 4(y24S - i2() - (b) Condense the following expression completely using the properties of logarithms: 3log(x) 4log(x +5) + log(9) — (s (b) ( X 3 \(X (x’j L L9 - (c) Solve for x: log() + log(x + 5) = I— I log(66) (c) - 0 5XflS ( ii(x- x Q.&c,tC - ( —U XSO ’ 3= 9 5 (d) Solve for x: 2e Give an exact solution do not use a calculator — - 5 (d) 9e 2 9 J S Qyifl +SiI° o — IISb Exam 03. Page 7 of 7 MathlO9O.004 19 April 2013 hat percent of a present amount of T 6. The half-life of radioactive radium is 1620 years. \\ radioactive radium will remain aft.er 870 years? (-jvC 6. (0i00 p o n t 2: e - /toZO (Z 4L1C) (7) / (0 ZO l00e 50/0O e 7. The population of Smalltown, has an initial population of 14,000 in the year 2000. The population grows at a rate of 3% per year. (a) Assuming exponential growth, write the population equation. 11000c. (a) J .03 LoO) 1 (o, /1 (b) What is the population in 2002? c20c9OOO ‘ ,ioOOe’ (b) osf) ? c?i?. ptf4fl (c)what year will the population be 35,000? (c) 3t 0 . 35O0O ’/oQOe 7 e° 03 0 1V &L.&/-