{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 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 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 31 "Homework due Thursday, 10
/13/05" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Section 10.5 " }{TEXT 
257 2 "#4" }{TEXT -1 103 ".  The [t,y(t)] coordinates plotted represen
t the number of yeast cells in a culture at time t (hours)." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "plot([[0,18],[2,39],[4,80],
[6,171],[8,336],[10,509],[12,597],[14,640],[16,664],[18,672]],x=0..20,
y=0..700,title=\"Number of yeast cells at time t (hours)\");" }}{PARA 
13 "" 1 "" {GLPLOT2D 529 185 185 {PLOTDATA 2 "6&-%'CURVESG6$7,7$$\"\"!
F)$\"#=F)7$$\"\"#F)$\"#RF)7$$\"\"%F)$\"#!)F)7$$\"\"'F)$\"$r\"F)7$$\"\"
)F)$\"$O$F)7$$\"#5F)$\"$4&F)7$$\"#7F)$\"$(fF)7$$\"#9F)$\"$S'F)7$$\"#;F
)$\"$k'F)7$F*$\"$s'F)-%'COLOURG6&%$RGBG$FB!\"\"F(F(-%&TITLEG6#QHNumber
~of~yeast~cells~at~time~t~(hours)6\"-%+AXESLABELSG6$Q\"xF[oQ\"yF[o-%%V
IEWG6$;F($\"#?F);F($\"$+(F)" 1 5 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
498 "(a)  Estimate the carrying capacity of the culture using the plot
.\n(b) Use the data to estimate the initial relative growth rate (look
 at the actual numbers plotted).\n(c) Find both an exponential model (
of the form y(t)=A*exp(kt)) and a logistic model (of the form y(t)=K/(
1+A*exp(-kt)) ) for the data points.\n(d) Compute the predicted values
 for each model for t=4, 8, 12 and 18.  How well do the models fit the
 data?\n(e) Use the logistic model to estimate the number of yeast cel
ls after 7 hours." }}}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Section 10.5 " }{TEXT 258 2 "#6" }
{TEXT -1 345 ".  Biologists stocked a lake with 400 fish and estimated
 the carrying capacity (the maximal population for the fish of that sp
ecies in the lake) to be 10,000.  The number of fish tripled in the fi
rst year.\n(a) Assuming that the size of the fish population satisfies
 the logistic equation, find an expression for the size of the populat
ion after " }{TEXT 259 1 "t" }{TEXT -1 74 " years.\n(b) How long will \+
it take for the population to increase to 5,000?" }}}}{MARK "7" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }