prcithce, iVIath 1090,OO3 uizO SP 2016 iiID #: Class ID #: Instructiolls: • Please clear your desks and remove headphones and hats during the quiz. • Show all work, as partial credit will be given where appropriate. If no work is shown, there may be no credit given. • All final answers should be written in the space provided on the quiz and in simplified form. When needed, give your answer as an exact amount, i.e. a fraction or symbolic expression, except for dollar amounts which should be rounded to the nearest cent. • Scientific calculators are allowed on this quiz. AXES! LABEL ALL LINES AND • If your phone is out during the quiz it will be considered a cheating offense put your phone away! 1 - Math 1090.002 62s 13 November 2015 1. Carbon-14 has a half-life of 5730 years. The amount y(t) of carbon-14 present after t years is given by y = yo() O where Yo is the initial amount present at t 18, 000 years, if the initial amount was 10 grams? 0 f1 = 0. How much is left after 10 ‘P-I (g’;ooo yectr t4# -t’o fivicl tf -, TrLIS (to) y: fL \2. tak-e4 p(u rl-ij (IOOO 6?3o Cence) Cttki;bn- , 7 Ayw 11 ic a1- €- 0 2 13 November 2015 Math 1090.002 2. For the function f(x) = 2 log (x) 5 — 1, answer the following: (5 (a) What is the domain of the functioi? (b) What is the x-intercept? (c) Sketch the graph of .1(x): (cc) VI1) x>O. por 29c()c_ 1 VXIR ‘ 1I1a(v?: (b sef f(x)o ()- I 5 O Z.ocj r 4 soIv- (b) (\r, o) 1001 Cx) 20 5f 14 -For CU x Lc& / cxe ¶ curv’eS J x-wre. Cx) ?u+ ‘4/’ - 4 to(I_ ::: ( j (I I) 3 ?j —1 (S)—ij 5 2o 2—I Ld\ (s (X’) — 35 2o I C -÷ ii -4- >c I -4- tJ Ii - LI 4 & I 3 0 4 cD + Q4) CD CD C CD C U) U) CD CD 0 CD C CD 0 0 CD CD C CD 01 CD CD CD z 0 CD CD 7. Solve these equations. (Note: Be sure to check your answers and state only the valid solutions.) (a)(1O points) 2 (x 3 log + 4 x—2)—log x=1 3 (: L4(C +V{ t(L4 Ic Cx 1? (Qv’L X-41X--2.. - oW’e +hMt +j’vZ, to t4(i(-2\ 2 (‘)( 93L> I ? t4x_X f4x-L_ - x x X hOt ( (b) (7 points) I’ 3 Kl (xlXL) 2 0— X I Solution(s): . ) 2 log(x)—llog(x uv pr’ope’f-tkL io )ot &)* (ft1t Cowb1v’ cpreccoV /t -xO 1 1Ox — ) X Solution(s): (c) (8 points) c*; 2000= 70 05 2000 • 1 ( )t_ tV 2 (Give answer rounded to nearest whole number.) XpDJ - (L0 —‘°°) )-(o0D =; p&/_l&o cEO } c Solution(s): 8 C C r) H ‘I - t (N (A; (0 (N C, 0 (A c-. / 0- S 1 ‘I 1 C:) 0- c J C-’ 2 * I II -4- I V. -J 3 0 2:5 c L ( iN N’ (J >( _.) —. (0 -1- N N c’y ( >( Mathematics of Finance Part 1: “Leave it Alone” Finances: Compound and Simple Interest t frLLS h- C ç1wL cZ- Description:7h or’oS -&€v 4z’-- pdd c__ur Sr-\ — Ci ((3Lt 1. Lk4Qd (V7f+1cP(Jj =iLeci o Three Scenarios: (1) Simple Interest: A (a) SC€cU a (b) fri wvq, es-f c-t W’Q i (d) Variables: • S= th-L • P • t r PM 0 -ti -the a n i+ia ( I pn ncp L ci. rL. a flV)L(CL - VV4-&Q t*4 XO(4-1Al (e) rpes of Questions: (LVS i’4” /L4fli 1 (h1e4’e+ Vaft U.rj jv.-ufit-f ,‘ S = P + t (Pr ) P (1 + rt) (c) Equation: • is nv s-1e4 d h-L ctvr 61 ec{ S14 r sl1rv is a ‘ dS Hc U 1/LC h (2) Compound Interest: tLrc’oI 2 sc,ivi’ i rivr4 (Y)VSl & irs i we SkCI d-t * ‘L .etrred e&-ecw-t fre t CLO I4A bf) SU frY (a) ECE41 -fl is. a tvi V L’w n-/ec€S1 (b) ) S=P(l+ — 1 (c) Equation: ‘5: Y’, (d) Variables: • S • P=ifQ • t = • r = • n i1 dCco L,LV’f = VcL4A-G ,‘rintpL —bhe Gf v-)k--v Cd LAIrZf 4 = vt- -L ot--f &-r5 t&ti h i.rn’J ct ./e4rS t4e4 ‘es-i d &( co t1”-’2 IUYlAf2 SU fri 15 rcrl-e rd (e) Types of Questions: WOt4’ VY) A CA- n— L I —QLf Cti lfrk o 1AIC fV\d I fl I LkJ) (3) Continuously Compound Interest: CnO-rfo.’ (a) -1-j irQ (1 v 4 1 iS n yecd cd• fl-i tt’i( 4IV COriy2 CYA’V’Oj 4 O7VtI’l ‘? j.-vrjt’e/ is -f’w, i cptI “/,rv’-d (c) W9re’e’com ‘1J41 (d)Equation:S=Pe •7- Drry) C-- (e) Variables: • S= ;i42j.t9, • P=—Lkt€ • = r = —/A • w’J,e+— C I’ThU 4, vau a-f â(L+ - OflW 4 1i0iS1 t’J I”- .‘ e. - ‘‘ cU? ci’iJid 1 itk (f) Types of Questions: 9 i-IeD4- c9 1 v’vwtUi rvw ve &LQ fr I hIti2 C’1t -Lft €?/vd 1-kjW Cl $i i /s tJ2/ 7 a-{ -‘‘ n’iJ J ctt /‘vt /21”2Od ‘ iAPY: What if we want to compare the totalinterest earned across multiple investment methods? (1) Simple Interest: APYzr (2) Periodic Compounding Interest: APY(1 +--) —1 (3) Continuously Compounding Interest: APY = er_i APY is the percent increase in your account over 1 year. i.e. the simple interest rate necessary to earn the amount of interest pe S P- -“‘ C’ -‘--1 a ,/ / v-M* (;frp ‘--‘ PQM c1 i (C Z;/ 7 I V(’(4 r i--; TQjv 0 C TVD aj?p, -t U0 / fr / J