Page 77 - Math SL HB Sem 1

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A crty is coccerued about pollutiou, and decides to look at the numbcr of peoplc
usrng raxis .At t}e end of the year 2000. t.here rver" ZSO ,"J i" th" crty. Alter z yeas
the uumber of taxrs- 1", in the city is grven by

T 280xl -72'
=
(u) (i) Filtd the rnunber oftaxis iu the city ar rie end of2005 .
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(ri) Fiod the year iu rvhiclr the munbsr of taxis is double the number of taxis
2
there wer€ at the ind of2000- An9: 00] .
[6 narbJ
(b) At rhe end of 2000 tlrere r.vsre 25 600 people ur the city s..ho used taxis
A1)er l years rhe nutrter of people, p,
in rlie .iry ,"fr" *"a ,iJ i" grr.* t y
r, - 2 560 000

(i) rP at rbe end of 2005. giving your alswer to tlle rearesr
:Tj,;TJ,*: ,4n( -_ ?4 6ic

fin5 nol doubiod
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(ii) A-fter seven complete years, will the value ofp be double its r,alue at dre
errd of2000? Jrxti$ your answ-er
[6 norksJ
G) Let X be tlrc ratio of tte aunrber ofpeople using taxrs in rlrc city to the auruber
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oftaxis. The city will reducc tfie rurmber ol tu*i" lf l < ZO.
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Fiod rtre lal.ue of R at fte eud of 2000
A-t'. C1s,.7
(ii) A:er lTw nuay courplere years rvill tte city first reduce tie mrmber
1,11,, arlt* lo
OI &lxl<,/ flaars
[5 marlcJ
t\
6 - The firnctions /(x) and g(-r) are deGled by /Cr)=.' a11d S(,r)=l)0+2_r)

G) IVrite do*"n f (r) t'1s .ln 1

O) (r) Frod (/"g)(x) Anrs. (t +2-^\

G) Fmd (/og)-I(:). A"s : 11

2