{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 256 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 
0 0 1 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 12 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 12 0 0 
0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 12 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
277 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 280 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 281 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
282 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 1 12 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 1 12 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 285 "" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 286 "" 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
287 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 1 12 0 
0 0 0 0 2 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T
imes" 1 12 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 
0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 
255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "H
eading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 
-1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 
}{PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 
0 0 0 0 1 }0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 
0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 
0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 
0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helveti
ca" 1 12 0 0 0 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 
}{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 
2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 3 
258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 
-1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 259 1 {CSTYLE "" -1 -1 "" 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "
" 4 260 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 261 1 {CSTYLE "" -1 -1 "" 1 
12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "" 4 262 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 
1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 263 1 {CSTYLE "" -1 
-1 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 
0 }{PSTYLE "" 4 264 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 
0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 4 265 1 {CSTYLE "" 
-1 -1 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 
-1 0 }}
{SECT 0 {PARA 258 "" 0 "" {TEXT -1 32 "Applications of Derivatives - I
I" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 18 "Calc
ulus I Project" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{SECT 0 {PARA 3 "" 
0 "" {TEXT -1 1 " " }{TEXT 256 11 "Objectives:" }}{PARA 0 "" 0 "" 
{TEXT -1 77 " To investigate population growth by examining the graphs
 of a function and  " }}{PARA 0 "" 0 "" {TEXT -1 16 " its derivative.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 0 "" }{TEXT 258 1 " " }}
{PARA 0 "" 0 "" {TEXT -1 80 " Using a computer algebra system you will
 draw the graphs of a given a function " }}{PARA 0 "" 0 "" {TEXT -1 
19 "and its derivative." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 259 15 "Solved Example:" }}
{PARA 0 "" 0 "" {TEXT -1 37 "Suppose the population P of the city " }
{TEXT 279 1 "t" }{TEXT -1 42 " years after 1990 is given (in thousands
) " }}{PARA 0 "" 0 "" {TEXT -1 10 "by      P(" }{TEXT 261 1 "t" }
{TEXT -1 10 ") = 25 - 2" }{TEXT 260 1 "t" }{TEXT -1 8 " + (0.5)" }
{XPPEDIT 18 0 "t^2;" "6#*$%\"tG\"\"#" }{TEXT -1 9 " - (.006)" }
{XPPEDIT 18 0 "t^3;" "6#*$%\"tG\"\"$" }}{PARA 0 "" 0 "" {TEXT -1 32 " \+
Answer the following questions." }}{PARA 0 "" 0 "" {TEXT -1 24 "a) Gra
ph the function P(" }{TEXT 262 1 "t" }{TEXT -1 33 ") and its derivativ
e function P'(" }{TEXT 263 1 "t" }{TEXT -1 2 ")." }}{PARA 0 "" 0 "" 
{TEXT -1 64 "b) During which years does the population increase in the
 1990s?" }}{PARA 0 "" 0 "" {TEXT -1 38 "c) Use the graph of the deriva
tive P'(" }{TEXT 264 1 "t" }{TEXT -1 32 ") to find the intervals where
 P(" }{TEXT 265 1 "t" }{TEXT -1 5 ") is " }}{PARA 0 "" 0 "" {TEXT -1 
29 "    increasing or decreasing." }}{PARA 0 "" 0 "" {TEXT -1 39 "d) A
t what interval on the graph of P'(" }{TEXT 266 1 "t" }{TEXT -1 43 ") \+
correspond to the time or times at which " }}{PARA 0 "" 0 "" {TEXT -1 
21 "    the population P(" }{TEXT 267 1 "t" }{TEXT -1 28 ") is increas
ing the fastest?" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 " " }{TEXT 
268 9 "Solution:" }{TEXT 269 1 " " }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 
1 " " }{TEXT 281 58 "a) Graph the function P(t) and its derivative fun
ction P'(" }{TEXT 280 1 "t" }{TEXT 282 2 ")." }}{PARA 0 "" 0 "" {TEXT 
-1 41 "  Activate the graphing package of Maple." }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 13 "with(plots);\n" }}{PARA 7 "" 1 "" {TEXT -1 50 
"Warning, the name changecoords has been redefined\n" }}{PARA 12 "" 1 
"" {XPPMATH 20 "6#7Z%(animateG%*animate3dG%-animatecurveG%&arrowG%-cha
ngecoordsG%,complexplotG%.complexplot3dG%*conformalG%,conformal3dG%,co
ntourplotG%.contourplot3dG%*coordplotG%,coordplot3dG%-cylinderplotG%,d
ensityplotG%(displayG%*display3dG%*fieldplotG%,fieldplot3dG%)gradplotG
%+gradplot3dG%,graphplot3dG%-implicitplotG%/implicitplot3dG%(inequalG%
,interactiveG%-listcontplotG%/listcontplot3dG%0listdensityplotG%)listp
lotG%+listplot3dG%+loglogplotG%(logplotG%+matrixplotG%(odeplotG%'paret
oG%,plotcompareG%*pointplotG%,pointplot3dG%*polarplotG%,polygonplotG%.
polygonplot3dG%4polyhedra_supportedG%.polyhedraplotG%'replotG%*rootloc
usG%,semilogplotG%+setoptionsG%-setoptions3dG%+spacecurveG%1sparsematr
ixplotG%+sphereplotG%)surfdataG%)textplotG%+textplot3dG%)tubeplotG" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "P := t -> 25 - 2*t + (0.5)*
t^2 - (.006)*t^3;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PGf*6#%\"tG
6\"6$%)operatorG%&arrowGF(,*\"#D\"\"\"*&\"\"#F.9$F.!\"\"*&$\"\"&F2F.)F
1F0F.F.*&$\"\"'!\"$F.)F1\"\"$F.F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "P1 := t -> diff(P(t),t);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#P1Gf*6#%\"tG6\"6$%)operatorG%&arrowGF(-%%diffG6$-%\"
PG6#9$F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(P1(
t));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,($\"\"#\"\"!!\"\"*&$\"#5F'
\"\"\"%\"tGF+F+*&$\"#=!\"$F+)F,F%F+F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "plot(\{P(t), P1(t)\}, t = 0..10);\n" }}{PARA 13 "" 1 
"" {GLPLOT2D 155 119 119 {PLOTDATA 2 "6&-%'CURVESG6$7S7$$\"\"!F)$\"#DF
)7$$\"3emmm;arz@!#=$\"3_#R5w0v(eC!#;7$$\"3[LL$e9ui2%F/$\"3t:**o$)=uECF
27$$\"3nmmm\"z_\"4iF/$\"33jkK-,&\\R#F27$$\"39ommT&phN)F/$\"3)*4MH4$RuO
#F27$$\"3KLLe*=)H\\5!#<$\"3^f&GM^)\\WBF27$$\"3smm\"z/3uC\"FE$\"3kFn2K^
:FBF27$$\"3!****\\7LRDX\"FE$\"3KfEDdo98BF27$$\"3%om;zR'ok;FE$\"3pVLRsQ
&GI#F27$$\"33++D1J:w=FE$\"3i&eSI_/oH#F27$$\"3oLLL3En$4#FE$\"3)f**GN?K
\\H#F27$$\"3#pmmT!RE&G#FE$\"3A*4kZ*z!pH#F27$$\"3D+++D.&4]#FE$\"3.'3&=m
=;.BF27$$\"3;+++vB_<FFE$\"3CO^\"Rp+PJ#F27$$\"33+++v'Hi#HFE$\"3C&\\cN+h
yK#F27$$\"3&om;z*ev:JFE$\"3\"G=#4Gq4WBF27$$\"3_LLL347TLFE$\"3I+\\lE>bn
BF27$$\"3nLLLLY.KNFE$\"3==_Kd'=4R#F27$$\"33++D\"o7Tv$FE$\"3\\K(pMs+@U#
F27$$\"3?LLL$Q*o]RFE$\"3ICq9k@E`CF27$$\"3m++D\"=lj;%FE$\"3mDk)yaj7\\#F
27$$\"3S++vV&R<P%FE$\"3tHhvJb7JDF27$$\"3CML$e9Ege%FE$\"3#HO<Be0ld#F27$
$\"3]LLeR\"3Gy%FE$\"3'4aJtGc:i#F27$$\"3emm;/T1&*\\FE$\"3)oU?bMUPn#F27$
$\"3=nm\"zRQb@&FE$\"338TP75'=t#F27$$\"3:++v=>Y2aFE$\"3;$3MPBpcy#F27$$
\"3Znm;zXu9cFE$\"3AxUGB[6ZGF27$$\"34+++]y))GeFE$\"3(e:uX'R>9HF27$$\"3H
++]i_QQgFE$\"3EDwWkWK$)HF27$$\"3b++D\"y%3TiFE$\"3/s$o')e\"[`IF27$$\"3+
++]P![hY'FE$\"3,6$*)>(*4^8$F27$$\"3iKLL$Qx$omFE$\"3.w\"G%*ps<@$F27$$\"
3Y+++v.I%)oFE$\"35?n=vk0(H$F27$$\"3?mm\"zpe*zqFE$\"3!*p(*)zzltP$F27$$
\"3;,++D\\'QH(FE$\"3'efJk3G%oMF27$$\"3%HL$e9S8&\\(FE$\"3)Qh`LD#>dNF27$
$\"3s++D1#=bq(FE$\"3kf*QRwPJl$F27$$\"3\"HLL$3s?6zFE$\"3enYs]V.]PF27$$
\"3a***\\7`Wl7)FE$\"3%=v]Tl<Z&QF27$$\"3enmmm*RRL)FE$\"31&yd\"=<keRF27$
$\"3%zmmTvJga)FE$\"3A?LmyE.oSF27$$\"3]MLe9tOc()FE$\"3[]^B0PfzTF27$$\"3
1,++]Qk\\*)FE$\"3!eSejSyZG%F27$$\"3![LL3dg6<*FE$\"328fd#QW%3WF27$$\"3%
ymmmw(Gp$*FE$\"3i#QBk[Q=_%F27$$\"3C++D\"oK0e*FE$\"3#3Xgo.0ck%F27$$\"35
,+v=5s#y*FE$\"3k)*=F6R!ow%F27$$\"#5F)$\"#\\F)-%'COLOURG6&%$RGBG$Ffz!\"
\"F(F(-F$6$7S7$F($!\"#F)7$F-$!3E6p+nO)Gy\"FE7$F4$!3cC3QnMO&f\"FE7$F9$!
3Q!eV\\OCgQ\"FE7$F>$!33npK[;&p<\"FE7$FC$!3W\")f[3H?0(*F/7$FI$!3NTYn^V+
1yF/7$FN$!3Yw!*3zLQaeF/7$FS$!3))4pWl&[>&QF/7$FX$!3GtkbB+1s=F/7$Fgn$\"3
5@)R(\\Q-x9!#>7$F\\o$\"3]&*HcT9g7>F/7$Fao$\"3=L)Q\\zZO)QF/7$Ffo$\"3o&Q
ZatOf%eF/7$F[p$\"3O\"*o/I\"*)4s(F/7$F`p$\"30>UR7285%*F/7$Fep$\"3c%\\*p
2`=S6FE7$Fjp$\"3CVTh(zzuI\"FE7$F_q$\"3-.m#[;K/]\"FE7$Fdq$\"3]W)oWMY(p;
FE7$Fiq$\"3O=kU-/\"R&=FE7$F^r$\"3\"f-fUi@x-#FE7$Fcr$\"36H&[7qcu?#FE7$F
hr$\"3!4<#)Hd`5P#FE7$F]s$\"3C[9)o7_fa#FE7$Fbs$\"3g!4uQE0fs#FE7$Fgs$\"3
UM3]>.8\")GFE7$F\\t$\"3-,'f(e\")GZIFE7$Fat$\"3m-#yd/@t@$FE7$Fft$\"3%3@
*3Cv1#Q$FE7$F[u$\"32%\\3[Fk*RNFE7$F`u$\"3QG%G&p([Nr$FE7$Feu$\"3i0alen'
z'QFE7$Fju$\"3#y%>CDd@JSFE7$F_v$\"33h4'\\-%pxTFE7$Fdv$\"3G'Q0_aciL%FE7
$Fiv$\"39!=XWSZR[%FE7$F^w$\"3#ppm8,onj%FE7$Fcw$\"3[(*fX<wj%y%FE7$Fhw$
\"3'G**=HY6y$\\FE7$F]x$\"3+&fU+(zv$3&FE7$Fbx$\"3^<')y'*ySJ_FE7$Fgx$\"3
;u5s!)eBw`FE7$F\\y$\"3AIoC*f8z]&FE7$Fay$\"3w!>X*=s<dcFE7$Ffy$\"3q$p$33
Q=*y&FE7$F[z$\"3h7I.lPPGfFE7$F`z$\"3uDv>p;4ggFE7$Fez$\"3;+++++++iFE-Fj
z6&F\\[lF(F][lF(-%+AXESLABELSG6$Q\"t6\"Q!F\\el-%%VIEWG6$;F(Fez%(DEFAUL
TG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" 
"Curve 2" }}}}}{PARA 0 "" 0 "" {TEXT -1 1 "." }}{SECT 0 {PARA 4 "" 0 "
" {TEXT 284 7 "Answers" }{TEXT -1 1 " " }{TEXT 283 9 "b) c) d) " }}
{PARA 0 "" 0 "" {TEXT 285 1 " " }{TEXT 288 0 "" }{TEXT -1 0 "" }{TEXT 
286 0 "" }{TEXT 287 0 "" }{TEXT -1 73 "b)  The graph of the function P
(t) is always increasing from  1992.  The " }}{PARA 0 "" 0 "" {TEXT 
-1 38 "       population increases from 1992." }}{PARA 260 "" 0 "" 
{TEXT -1 69 "c)   P'(t) is negative from 1900 to 1992.  This means the
 population " }}{PARA 261 "" 0 "" {TEXT -1 78 "      decreases from 19
90 to 1992.  P'(t) is zero at 1992.  This implies that " }}{PARA 262 "
" 0 "" {TEXT -1 80 "      the population has reached its minimum.  P'(
t) is positive and increasing " }}{PARA 263 "" 0 "" {TEXT -1 76 "     \+
 from 1992 always positive which means the graph is above the x-axis. \+
 " }}{PARA 264 "" 0 "" {TEXT -1 80 "      Thus the graph of P'(t) conf
irms that P(t) is increasing through the time " }}{PARA 265 "" 0 "" 
{TEXT -1 29 "       period [1992, 2000].  " }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "d)  P(t) increases at increasin
g rate on the interval [2, 10], since the graph " }}{PARA 0 "" 0 "" 
{TEXT -1 78 "     of P'(t) is positive and increasing on [2, 10].  The
 rate of increase in " }}{PARA 0 "" 0 "" {TEXT -1 79 "      population
 is the highest at t = 10 since P'(t) is the highest at t = 10 " }}
{PARA 0 "" 0 "" {TEXT -1 19 "     or year 2000. " }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{PARA 5 "" 0 "" {TEXT -1 64 "________________________
________________________________________" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 259 "" 0 "" {TEXT -1 10 "ASSIGNMENT" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 1 " " }{TEXT 270 8 "P
roblem:" }}{PARA 0 "" 0 "" {TEXT -1 37 "Suppose the population P of th
e city " }{TEXT 278 1 "t" }{TEXT -1 42 " years after 1990 is given (in
 thousands) " }}{PARA 0 "" 0 "" {TEXT -1 17 "by             P(" }
{TEXT 271 1 "t" }{TEXT -1 8 ") = 10 +" }{TEXT 272 2 " t" }{TEXT -1 8 "
 - (0.1)" }{XPPEDIT 18 0 "t^2;" "6#*$%\"tG\"\"#" }{TEXT -1 9 "  + (.01
)" }{XPPEDIT 18 0 "t^3;" "6#*$%\"tG\"\"$" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "a) Graph the function P(" }{TEXT 
273 1 "t" }{TEXT -1 33 ") and its derivative function P'(" }{TEXT 274 
1 "t" }{TEXT -1 2 ")." }}{PARA 0 "" 0 "" {TEXT -1 18 "b) Is the graph \+
P(" }{TEXT 275 1 "t" }{TEXT -1 34 ") increasing throughout the 1990s?
" }}{PARA 0 "" 0 "" {TEXT -1 39 "c) At what interval on the graph of P
'(" }{TEXT 276 1 "t" }{TEXT -1 43 ") correspond to the time or times a
t which " }}{PARA 0 "" 0 "" {TEXT -1 21 "    the population P(" }
{TEXT 277 1 "t" }{TEXT -1 28 ") is increasing the fastest?" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 " ______________
____________________________________________________" }}{PARA 0 "" 0 "
" {TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 99 "MSIP Grant #P120A8008
9-98:  \"Three Urban Calculus Reform programs: Adopting the Best\" 199
8-2001    " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 3 "   " }}}{MARK "1 0" 0 }{VIEWOPTS 1 1 
0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }