Note: For all questions, answer (E) NOTA means none of the above answers is correct.
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1 Thea Logarihms & Eponens 0 ΜΑΘ Naional Convenion Noe: For all quesions, answer means none of he above answers is correc.. The elemen C 4 has a half life of 70 ears. There is grams of C 4 in a paricular sample now. Which of he following gives he correc amoun of C ears from now? (A) 400 grams 0 grams grams (D) 0 grams. A scienis adds a small amoun of baceria o a growh medium on Da 0. On Da 4, he scienis deermines ha he populaion of baceria has quadrupled from is original value. If he populaion grows eponeniall in ime, which of he following is closes o he da he scienis can epec he populaion o be one million imes is iniial value? (A) Da 0 Da 40 Da 0 (D) Da 0. Wha is he unis digi of 0? (A) 7 (D) 9 (, find he value of b if f ( 0) and f ( ) 0. b 4. If f ) a (A) 7 log0 (D) 6. Wrie an equaion in erms of for he area of a recangle bounded b he graph of e and he ais. The recangle is siuaed so ha one of he sides lies along he ais, he side adjacen o his side is parallel o he ais, and wo adjacen verices of he recangle lies on he graph of e. (A) A e A e A e (D) A e 6. Given ha 0, epand compleel: ln (A) ln ln ln ln ln ln 4ln ln ln ln ln (D) 4ln ln ln ln ln Page of
2 Thea Logarihms & Eponens 0 ΜΑΘ Naional Convenion 7. Wha is he value of r r if. 0? (A) r 0 (D) 0. Consider he eponenial funcion C below (where 0 represens he iniial ime) and choose he correc saemen. C (A) C describes eponenial growh and he iniial amoun is 00. C describes eponenial deca and he iniial amoun is 00. C describes eponenial growh and he iniial amoun is.6 (D) C describes eponenial deca and he iniial amoun is.6 9. Your mah eacher has asked ou o solve log 6 4 log for. Which of he following equaions has he same posiive soluion(s) as he logarihmic equaion? (A) (D) 6 0. Consider he quadraic funcion f,log,,log, 4,log 4 ha passes hrough o be an approimaion of F( ) log. Esimae he value of log b evaluaing f () o four decimal places. (A) (D).000. A few weeks ino he SARS (Severe Acue Respiraor Sndrome) epidemic of 00, he World Healh Organizaion (WHO) deermined ha he rae of infecion was increasing a a rae of 4% per da. Approimael 00 people had been infeced b April, 00. Assuming an eponenial model, deermine when he WHO could epec he number of infeced persons o reach 700 people. (A) April 4, 00 April, 00 Ma, 00 (D) June 6, 00. Evaluae: log 04 4 j j (A) (D) 00 Page of
3 Thea Logarihms & Eponens 0 ΜΑΘ Naional Convenion. Which of he following eponenial equaions models our salar s (in dollars per hour) over ime (in ears) given he following condiion: You ge a job paing $0 per hour. Each ear our salar goes up b % o keep up wih he cos of living. (A) s ( ) 0(.0) s ( ) 0(.0) s ( ) 0(.0) (D) s ( ) (.0) 4. Which of he following saemen(s) is/are rue? 4 4 I. n n II. 00 n0 n IV. i i0 j0 99 i i V. k k k0 k0 III. k k0 k0 k (A)I, III, V I I, II, III, IV, V (D) I, V. Calculae he raio if log log log, where 0. (A) or 4 (D) 4 6. Consider f ( ) logb and g( ) log where 0 b. Which of he following mus b be rue? I. The graphs of =f() and =g() are mirror images of each oher wih respec o he ais. II. The poin (,0) is on he graph of =f() and =g(). III. The poin (b,) is on he graph of =f() and =g(). IV. Given ha is a posiive real number, he range of f and g is he se of real numbers. V. Boh funcions f and g are one o one. (A) I, II, IV, V I, II, III, IV II, IV, V (D) I, II, III, IV, V 7. There eis posiive inegers M, A, and T wih no wo of which having common facors greaer han such ha M log6 7 Alog6 T. Wha is he value of M+A+T? (A) 9 0 (D) 0 Page of
4 Thea Logarihms & Eponens 0 ΜΑΘ Naional Convenion n. Solve for : log ( n ) (A) 4 4 (D) n 9. Evaluae: log 4 n n (A) 6 (D) 0. How man real soluions does 0 log have? (A) 0 (D) Infiniel man.. How does he graph of ln( ) compare wih he graph of he paren funcion ln? (A) Translaed up unis and righ unis. Translaed up unis and lef unis. Translaed up unis and righ unis. (D) Translaed up unis and lef unis.. In an old elevision commercial, a woman who liked her shampoo so much ha she old wo people, and each of hem old wo people, and each of hem old wo people, ec. Suppose here are 0 such levels of elling and ha everone who hears of he shampoo does use i and does ell wo friends. How man shampoo users (including he original woman) would be in his group? (A) (D) 04. If 47, find he value of. (A) (D) If log k, epress log in erms of k. (A) 6k 6k k 9 (D) k Page 4 of
5 Thea Logarihms & Eponens 0 ΜΑΘ Naional Convenion. If log. 00 and log. 477 hen which of he following is closes o he value of, given ha? (A) (D) If 9 and and are inegers, deermine he value of. (A) (D) e have? 9 7. How man real soluions does (A) 0 (D) log. If f 4 and g log evaluae g (A) f. log log (D) Le f. Evaluae log f log for values which f () converges. (A) (D) 0 0. The sum of he firs wo erms of a seven erm geomeric sequence is 0, and he sum of he sum of he las wo erms is. Find he sum of all seven erms of he sequence. (A) (D) 6 Page of
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